Items tagged with dsolve

hi

please help me for solve differential equations

6.mw
 

Typesetting:-mrow(Typesetting:-mi("dsys5", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("≔", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mi("h3", italic = "true", mathvariant = "italic"), Typesetting:-mo("⁡", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("θ", italic = "false", mathvariant = "normal")), mathvariant = "normal")), Typesetting:-mo("⁢", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mn("1.66560413123239", mathvariant = "normal"), Typesetting:-mo("⁢", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mn("10", mathvariant = "normal"), Typesetting:-mn("-13", mathvariant = "normal"), superscriptshift = "0")), Typesetting:-mo("−", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mn("6.04408313000100", mathvariant = "normal"), Typesetting:-mo("⁢", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mn("10", mathvariant = "normal"), Typesetting:-mn("-18", mathvariant = "normal"), superscriptshift = "0")), Typesetting:-mo("⁢", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mi("ω", italic = "false", mathvariant = "normal"), Typesetting:-mn("2", mathvariant = "normal"), superscriptshift = "0"))), mathvariant = "normal")), Typesetting:-mo("−", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mn("3.61156743942916", mathvariant = "normal"), Typesetting:-mo("⁢", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mn("10", mathvariant = "normal"), Typesetting:-mn("-16", mathvariant = "normal"), superscriptshift = "0")), Typesetting:-mo("⁢", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-msup(Typesetting:-mo("ⅆ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("2", mathvariant = "normal"), superscriptshift = "0")), Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mo("ⅆ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mi("θ", italic = "false", mathvariant = "normal"), Typesetting:-mn("2", mathvariant = "normal"), superscriptshift = "0"))), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false"), Typesetting:-mo("⁢", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mrow(Typesetting:-mi("h3", italic = "true", mathvariant = "italic"), Typesetting:-mo("⁡", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("θ", italic = "false", mathvariant = "normal")), mathvariant = "normal"))), mathvariant = "normal")), Typesetting:-mo("+", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mn("3.34243067273144", mathvariant = "normal"), Typesetting:-mo("⁢", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mn("10", mathvariant = "normal"), Typesetting:-mn("-20", mathvariant = "normal"), superscriptshift = "0")), Typesetting:-mo("⁢", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-msup(Typesetting:-mo("ⅆ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("4", mathvariant = "normal"), superscriptshift = "0")), Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mo("ⅆ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mi("θ", italic = "false", mathvariant = "normal"), Typesetting:-mn("4", mathvariant = "normal"), superscriptshift = "0"))), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false"), Typesetting:-mo("⁢", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mrow(Typesetting:-mi("h3", italic = "true", mathvariant = "italic"), Typesetting:-mo("⁡", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("θ", italic = "false", mathvariant = "normal")), mathvariant = "normal"))), mathvariant = "normal")), Typesetting:-mo("−", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mn("2.11542909550035", mathvariant = "normal"), Typesetting:-mo("⁢", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mn("10", mathvariant = "normal"), Typesetting:-mn("-23", mathvariant = "normal"), superscriptshift = "0")), Typesetting:-mo("⁢", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-msup(Typesetting:-mo("ⅆ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("6", mathvariant = "normal"), superscriptshift = "0")), Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mo("ⅆ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mi("θ", italic = "false", mathvariant = "normal"), Typesetting:-mn("6", mathvariant = "normal"), superscriptshift = "0"))), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false"), Typesetting:-mo("⁢", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mrow(Typesetting:-mi("h3", italic = "true", mathvariant = "italic"), Typesetting:-mo("⁡", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("θ", italic = "false", mathvariant = "normal")), mathvariant = "normal"))), mathvariant = "normal"))), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mi("h3", italic = "true", mathvariant = "italic"), Typesetting:-mo("⁡", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", mathvariant = "normal")), mathvariant = "normal")), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("0", mathvariant = "normal")), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mi("h3", italic = "true", mathvariant = "italic"), Typesetting:-mo("⁡", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal")), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("0", mathvariant = "normal")), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mi("D", italic = "false", mathvariant = "normal"), Typesetting:-mo("⁡", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("h3", italic = "true", mathvariant = "italic")), mathvariant = "normal")), Typesetting:-mo("⁡", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", mathvariant = "normal")), mathvariant = "normal")), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("0", mathvariant = "normal")), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mi("D", italic = "false", mathvariant = "normal"), Typesetting:-mo("⁡", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("h3", italic = "true", mathvariant = "italic")), mathvariant = "normal")), Typesetting:-mo("⁡", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal")), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("0", mathvariant = "normal")), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("D", italic = "false", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mn("3", mathvariant = "normal"), mathvariant = "normal"), superscriptshift = "0", Typesetting:-msemantics = "@@"), Typesetting:-mo("⁡", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("h3", italic = "true", mathvariant = "italic")), mathvariant = "normal")), Typesetting:-mo("⁡", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", mathvariant = "normal")), mathvariant = "normal")), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("0", mathvariant = "normal")), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("D", italic = "false", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mn("3", mathvariant = "normal"), mathvariant = "normal"), superscriptshift = "0", Typesetting:-msemantics = "@@"), Typesetting:-mo("⁡", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("h3", italic = "true", mathvariant = "italic")), mathvariant = "normal")), Typesetting:-mo("⁡", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal")), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("0", mathvariant = "normal"))), mathvariant = "normal", open = "{", close = "}"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mi("dsys6", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("≔", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("subs", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("omega", italic = "false", mathvariant = "normal"), Typesetting:-mo("^", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.1111111em", rspace = "0.1111111em"), Typesetting:-mn("2", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("omega2", italic = "true", mathvariant = "italic"), Typesetting:-mo("⋅", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mn("10", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mn("25", mathvariant = "normal")), superscriptshift = "0"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("dsys5", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("syss", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("bcss", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("≔", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("selectremove", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("has", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("dsys6", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("diff", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mi("indets", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("syss", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("specfunc", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("diff", italic = "true", mathvariant = "italic")), mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mi("solve", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("syss", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("diff", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("h3", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("θ", italic = "false", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("θ", italic = "false", mathvariant = "normal"), Typesetting:-mo("$", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("6", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "{", close = "}")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", italic = "true", mathvariant = "italic", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("extra_bcss", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("≔", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("seq", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("seq", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("D", italic = "false", mathvariant = "normal"), Typesetting:-mo("@@", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("i", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("h3", italic = "true", mathvariant = "italic")), mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("a", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("i", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("5", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("a", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "{", close = "}"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("minus", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("lhs", italic = "true", mathvariant = "italic"), Typesetting:-mo("~", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.1111111em", rspace = "0.1111111em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("bcss", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo("for", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("bbb", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("in", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("extra_bcss", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("do", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("try", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("print", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("bbb", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("ress", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("bbb", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo("≔", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("dsolve", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("dsys6", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("union", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("bbb", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn(".0000001", mathvariant = "normal")), mathvariant = "normal", open = "{", close = "}"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("numeric", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("method", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("bvp", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("middefer", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("approxsoln", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("omega2", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.0000001", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("h3", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("θ", italic = "false", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mi("θ", italic = "false", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mn("4", mathvariant = "normal")), superscriptshift = "0"), Typesetting:-mo("*", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.1666667em", rspace = "0.1666667em"), Typesetting:-msup(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo("−", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mi("θ", italic = "false", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mn("4", mathvariant = "normal")), superscriptshift = "0")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("output", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("listprocedure", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("initmesh", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("3024", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("abserr", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("1e−2", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("catch", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("print", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("lasterror", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("end", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("try", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("end", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("do", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("indx", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("≔", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("indices", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("ress", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("nolist", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mi("nops", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("ress", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("seq", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("subs", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("ress", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("i", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("omega2", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mi("nops", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mi("RESS", italic = "true", mathvariant = "italic"), Typesetting:-mo("≔", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("ress", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("D", italic = "false", mathvariant = "normal"), Typesetting:-mo("@@", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("2", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("h3", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("RESS", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("fy", italic = "true", mathvariant = "italic"), Typesetting:-mo("≔", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("eval", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("h3", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("θ", italic = "false", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("RESS", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("with", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("CurveFitting", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("g3", italic = "true", mathvariant = "italic"), Typesetting:-mo("≔", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("PolynomialInterpolation", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("fy", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn(".1", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("fy", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0.1", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn(".2", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("fy", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0.2", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0.3", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("fy", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0.3", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn(".4", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("fy", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0.4", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn(".5", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("fy", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0.5", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0.6", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("fy", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0.6", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0.7", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("fy", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0.7", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0.8", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("fy", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0.8", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0.9", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("fy", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0.9", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("fy", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal"))

-27557.32319*fy(.1)*x^10+578703.7033*fy(.6)*x^10+2755.731922*fy(1)*x^10-27557.31922*fy(.9)*x^10+124007.9365*fy(.8)*x^10-330687.8301*fy(.7)*x^10-694444.4435*fy(.5)*x^10+578703.7011*fy(.4)*x^10+124007.9238*fy(.2)*x^10+2755.734127*fy(0)*x^10-330687.8474*fy(.3)*x^10+23974.86773*fy(1)*x^8-249669.3122*fy(.9)*x^8+1170634.921*fy(.8)*x^8-3253968.249*fy(.7)*x^8-7430555.546*fy(.5)*x^8+6458333.316*fy(.4)*x^8+1505456.227*fy(.2)*x^8+36375.68428*fy(0)*x^8-3849206.511*fy(.3)*x^8-348875.7026*fy(.1)*x^8+5937499.995*fy(.6)*x^8-12400.79365*fy(1)*x^9+126763.6684*fy(.9)*x^9-582837.3016*fy(.8)*x^9+1587301.585*fy(.7)*x^9+3472222.217*fy(.5)*x^9-2951388.878*fy(.4)*x^9-657242.0034*fy(.2)*x^9-15156.53643*fy(0)*x^9+1719576.799*fy(.3)*x^9+148809.5434*fy(.1)*x^9-2835648.146*fy(.6)*x^9+fy(0)-26041.66666*fy(1)*x^7+275462.9630*fy(.9)*x^7-1314236.111*fy(.8)*x^7+3724206.344*fy(.7)*x^7+8888888.878*fy(.5)*x^7-7920138.872*fy(.4)*x^7-1949652.641*fy(.2)*x^7-50016.56146*fy(0)*x^7+4847222.406*fy(.3)*x^7+465277.8258*fy(.1)*x^7-6940972.216*fy(.6)*x^7-7421.875001*fy(1)*x^5+80405.09258*fy(.9)*x^5-394522.5694*fy(.8)*x^5+1155694.443*fy(.7)*x^5+3008263.885*fy(.5)*x^5-2835295.136*fy(.4)*x^5-805303.7775*fy(.2)*x^5-24858.22656*fy(0)*x^5+1854027.834*fy(.3)*x^5+209756.9599*fy(.1)*x^5-2240746.526*fy(.6)*x^5+17436.34259*fy(1)*x^6-186863.4259*fy(.9)*x^6+905121.5276*fy(.8)*x^6-2610416.664*fy(.7)*x^6-6512013.882*fy(.5)*x^6+5962326.380*fy(.4)*x^6+1566579.766*fy(.2)*x^6+43478.02887*fy(0)*x^6-3763194.572*fy(.3)*x^6-388252.3492*fy(.1)*x^6+4965798.607*fy(.6)*x^6+28.28968254*fy(1)*x^2-313.0952381*fy(.9)*x^2+1577.232143*fy(.8)*x^2-4776.190470*fy(.7)*x^2-13753.99998*fy(.5)*x^2+14064.58332*fy(.4)*x^2+5465.178399*fy(.2)*x^2+351.4544056*fy(0)*x^2-10382.53991*fy(.3)*x^2-1928.968320*fy(.1)*x^2+9668.055554*fy(.6)*x^2-323.1646826*fy(1)*x^3+3557.164903*fy(.9)*x^3-17797.76786*fy(.8)*x^3+53426.19041*fy(.7)*x^3+149624.9998*fy(.5)*x^3-149352.0832*fy(.4)*x^3-51751.33736*fy(.2)*x^3-2317.433202*fy(0)*x^3+105973.2830*fy(.3)*x^3+15855.75470*fy(.1)*x^3-106895.6018*fy(.6)*x^3+1994.268078*fy(1)*x^4-21796.84744*fy(.9)*x^4+108108.3829*fy(.8)*x^4-320951.0578*fy(.7)*x^4-868736.1101*fy(.5)*x^4+843271.9899*fy(.4)*x^4+262665.6630*fy(.2)*x^4+9416.145650*fy(0)*x^4-573728.8516*fy(.3)*x^4-73185.74068*fy(.1)*x^4+632942.1292*fy(.6)*x^4-1.000000000*fy(1)*x+11.11111111*fy(.9)*x-56.24999998*fy(.8)*x+171.4285712*fy(.7)*x+503.9999992*fy(.5)*x-524.9999996*fy(.4)*x-224.9999938*fy(.2)*x-29.28968402*fy(0)*x+400.0000082*fy(.3)*x+100.0000024*fy(.1)*x-350.0000000*fy(.6)*x

(1)

``


 

Download 6.mw

 

hi every body...

general solution of six order differential equation for example following equation

diff(w(x), x, x, x, x, x, x)+A*(diff(w(x), x, x, x, x))+B*(diff(w(x), x, x))+(-chi*omega^2+C)*w(x) = 0

is 

w := C1*sinh(upsilon*x)+C2*cosh(upsilon*x)+C3*sin(kappa*x)+C4*cos(kappa*x)+C5*sin(varsigma*x)+C6*cos(varsigma*x)

??

OR

w := C1*(cosh(upsilon*x)-sinh(upsilon*x))+C2*(cosh(upsilon*x)+sinh(upsilon*x))+C3*(cosh(kappa*x)-sinh(kappa*x))+C4*(cosh(kappa*x)+sinh(kappa*x))+C5*(cosh(varsigma*x)-sinh(varsigma*x))+C6*(cosh(varsigma*x)+sinh(varsigma*x))

or another form? is correct both of them or no??

please see maple attaced file.

please help me

thanks...

3.mw
 

restart; dsys3 := diff(w(x), x, x, x, x, x, x)+A*(diff(w(x), x, x, x, x))+B*(diff(w(x), x, x))+(-chi*omega^2+C)*w(x) = 0

diff(diff(diff(diff(diff(diff(w(x), x), x), x), x), x), x)+A*(diff(diff(diff(diff(w(x), x), x), x), x))+B*(diff(diff(w(x), x), x))+(-chi*omega^2+C)*w(x) = 0

(1)

dsol5 := dsolve(dsys3):

H := subs(36*B*A+108*chi*omega^2-108*C-8*A^3+12*sqrt(-12*A^3*chi*omega^2+81*chi^2*omega^4+54*A*B*chi*omega^2+12*A^3*C-3*A^2*B^2-162*C*chi*omega^2-54*A*B*C+12*B^3+81*C^2) = E, (4*I)*A^2*sqrt(3)-I*sqrt(3)*E^(2/3)-(12*I)*B*sqrt(3)-4*A^2-4*A*E^(1/3)-E^(2/3)+12*B = F, (4*I)*A^2*sqrt(3)-I*sqrt(3)*E^(2/3)-(12*I)*B*sqrt(3)+4*A^2+4*A*E^(1/3)+E^(2/3)-12*B = G, 4*A^2-2*A*E^(1/3)+E^(2/3)-12*B = S, rhs(dsol5))

 

_C1*exp(-(1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3))+_C2*exp((1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3))+_C3*exp(-(1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3))+_C4*exp((1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3))+_C5*exp(-(1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3))+_C6*exp((1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3))

(2)

convert(H, trig)

_C1*(cosh((1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3))-sinh((1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3)))+_C2*(cosh((1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3))+sinh((1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3)))+_C3*(cosh((1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3))-sinh((1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3)))+_C4*(cosh((1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3))+sinh((1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3)))+_C5*(cosh((1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3))-sinh((1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3)))+_C6*(cosh((1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3))+sinh((1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3)))

(3)

NULL

``


 

Download 3.mw

 

 

hi ..how i can rewrite answer in compressive format. that result seen readible and incomplex.for example how i can use change of variable, in order to final result has a short format...

thanks1.mw

 


 

dsolve({Q(0) = 0, Q(t) = (1.375*4190)*(80-T__1(t)), Q(t) = (1.375*4190)*(T__2(t)-38.2), diff(Q(t), t) = (240*0.1375e-1)*(T__1s(t)-T__2s(t))/(0.1e-2), diff(Q(t), t) = (0.1375e-1*47.6035070726347)*(T__1(t)-T__1s(t))*(T__1(t)+T__1s(t))^.438263122318020*((T__1(t)-T__1s(t))^.327228811371115), diff(Q(t), t) = (0.1375e-1*47.6035072491656)*(T__2s(t)-T__2(t))*(T__2(t)+T__2s(t))^.438263121701134*((T__2s(t)-T__2(t))^.327228811154163)}, numeric)

could you help with this? maybe because of too long exponents or just a maple bug?

when i try to solve this DAE it just crash. it says connection with kernel has been lost, and tells me to look for online help.

thank you very much...
 

Download crash_ecuation.mwcrash_ecuation.mw

dsolve(f(x,y),y(x),parametric) in Maple 9.5 outputs an expression for y(_T) and for x(_T).

(from the book "Computer Algebra Recipes for Mathematical Physics by Richard H. Enns, section 7.1.1, finding the parametric equation of the brachistochrone)

but the same command in Maple 2016 outputs an expression for y(x) only.

Why do Maple 9.5 and Maple 2016 produce different output?

Where can I find a help page explaining or giving examples of dsolve, parametric?

 

Please anyone, I have been battling with this problem for a while yet the error message keeps coming. Would be happy if responded to.

Thanks 
 

NULL

restart

Digits := 10

with(ODETools)

with(student)

with(plots)

inf := 4.2

NULL

equ1 := diff(f[0](eta), `$`(eta, 3))+theta[0](eta) = 0

equ2 := diff(theta[0](eta), `$`(eta, 2))+3*f[0](eta)*(diff(theta[0](eta), eta)) = 0

Bcs1 := f[0](0) = 0, (D(f[0]))(0) = 0, theta[0](0) = 1, theta[0](inf) = 0, (D(D(f[0])))(inf) = 0

S1 := dsolve({Bcs1, equ1, equ2}, {f[0](eta), theta[0](eta)}, type = numeric)

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(21, {(1) = .0, (2) = .19993050946471785, (3) = .40078377746315347, (4) = .6025727748609847, (5) = .805792602032412, (6) = 1.010942304650061, (7) = 1.2180763336987108, (8) = 1.4270038908463605, (9) = 1.6375902221831404, (10) = 1.8498543724186098, (11) = 2.0633079120179274, (12) = 2.277741391439103, (13) = 2.4931129139047408, (14) = 2.7089887386097495, (15) = 2.9252757828996607, (16) = 3.1419082091550377, (17) = 3.3586565343807853, (18) = 3.5755020065597023, (19) = 3.7897835066856795, (20) = 3.99778821105096, (21) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(21, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .8245101724754578, (1, 4) = 1.0, (1, 5) = -.7109880345825436, (2, 1) = 0.15194130384185354e-1, (2, 2) = .14580548143397778, (2, 3) = .6387850483082825, (2, 4) = .857963238913636, (2, 5) = -.7087869877011237, (3, 1) = 0.5625387147295941e-1, (3, 2) = .2577556073775664, (3, 3) = .4806893773780191, (3, 4) = .7167515674300292, (3, 5) = -.6944757971749999, (4, 1) = .11711872046127954, (4, 2) = .34110224456170846, (4, 3) = .3499979513587831, (4, 4) = .5797495081496531, (4, 5) = -.6595302165926753, (5, 1) = .19289982468547776, (5, 2) = .4011617938545637, (5, 3) = .24543411078038904, (5, 4) = .4513251759894287, (5, 5) = -.6004288125540566, (6, 1) = .2797565188640971, (6, 2) = .4428520778243424, (6, 3) = .16494373679100188, (6, 4) = .3361497197458259, (6, 5) = -.5193790217421129, (7, 1) = .37456519619918616, (7, 2) = .4705413231882741, (7, 3) = .10579089990103963, (7, 4) = .23830615973840436, (7, 5) = -.4239568572171149, (8, 1) = .4748530263492926, (8, 2) = .48804935564305746, (8, 3) = 0.6453023961994517e-1, (8, 4) = .16012402142182885, (8, 5) = -.3249339143694787, (9, 1) = .5788362246256302, (9, 2) = .4985566327609869, (9, 3) = 0.37313069594910674e-1, (9, 4) = .10159768333703968, (9, 5) = -.2329675184040786, (10, 1) = .6853588708527928, (10, 2) = .504526521398875, (10, 3) = 0.20382679676615986e-1, (10, 4) = 0.606567047794537e-1, (10, 5) = -.1557809847294323, (11, 1) = .7934302125147107, (11, 2) = .5077218117791161, (11, 3) = 0.10501648422412073e-1, (11, 4) = 0.3401535257794869e-1, (11, 5) = -0.9702883361504151e-1, (12, 1) = .9024960382686785, (12, 2) = .5093322596657791, (12, 3) = 0.5093151483295916e-2, (12, 4) = 0.17884998462519692e-1, (12, 5) = -0.5623455808801906e-1, (13, 1) = 1.012284543110573, (13, 2) = .5100955651640168, (13, 3) = 0.23195437904716377e-2, (13, 4) = 0.8800007896506692e-2, (13, 5) = -0.3029419520059991e-1, (14, 1) = 1.1224435496090202, (14, 2) = .5104345698316491, (14, 3) = 0.9909285667744439e-3, (14, 4) = 0.4050636647573417e-2, (14, 5) = -0.1517584553753996e-1, (15, 1) = 1.2328614831160174, (15, 2) = .5105756222550529, (15, 3) = 0.395898479049903e-3, (15, 4) = 0.17420870540071946e-2, (15, 5) = -0.70679676150117755e-2, (16, 1) = 1.3434756128476715, (16, 2) = .5106303954198085, (16, 3) = 0.147062675323547e-3, (16, 4) = 0.6987853715227916e-3, (16, 5) = -0.3059943628543717e-2, (17, 1) = 1.4541564025817688, (17, 2) = .5106500758344735, (17, 3) = 0.5016782526067641e-4, (17, 4) = 0.2606614231585554e-3, (17, 5) = -0.12322310129648298e-2, (18, 1) = 1.5648893907808388, (18, 2) = .5106565008224614, (18, 3) = 0.15188983867428313e-4, (18, 4) = 0.8947015334152312e-4, (18, 5) = -0.4615493175592657e-3, (19, 1) = 1.6743138673548472, (19, 2) = .5106582990190938, (19, 3) = 0.3766036798992976e-5, (19, 4) = 0.27659825670281336e-4, (19, 5) = -0.16295043631438081e-3, (20, 1) = 1.780533246301514, (20, 2) = .5106586754129524, (20, 3) = 0.5632933568740209e-6, (20, 4) = 0.6803446974353735e-5, (20, 5) = -0.55451472121262876e-4, (21, 1) = 1.883794455897945, (21, 2) = .5106587096287567, (21, 3) = .0, (21, 4) = .0, (21, 5) = -0.18247231920817762e-4}, datatype = float[8], order = C_order); YP := Matrix(21, 5, {(1, 1) = .0, (1, 2) = .8245101724754578, (1, 3) = -1.0, (1, 4) = -.7109880345825436, (1, 5) = .0, (2, 1) = .14580548143397778, (2, 2) = .6387850483082825, (2, 3) = -.857963238913636, (2, 4) = -.7087869877011237, (2, 5) = 0.3230820571723456e-1, (3, 1) = .2577556073775664, (3, 2) = .4806893773780191, (3, 3) = -.7167515674300292, (3, 4) = -.6944757971749999, (3, 5) = .11720085670609043, (4, 1) = .34110224456170846, (4, 2) = .3499979513587831, (4, 3) = -.5797495081496531, (4, 4) = -.6595302165926753, (4, 5) = .23173000521865406, (5, 1) = .4011617938545637, (5, 2) = .24543411078038904, (5, 3) = -.4513251759894287, (5, 4) = -.6004288125540566, (5, 5) = .3474678380333613, (6, 1) = .4428520778243424, (6, 2) = .16494373679100188, (6, 3) = -.3361497197458259, (6, 4) = -.5193790217421129, (6, 5) = .4358990012808411, (7, 1) = .4705413231882741, (7, 2) = .10579089990103963, (7, 3) = -.23830615973840436, (7, 4) = -.4239568572171149, (7, 5) = .47639845021055693, (8, 1) = .48804935564305746, (8, 2) = 0.6453023961994517e-1, (8, 3) = -.16012402142182885, (8, 4) = -.3249339143694787, (8, 5) = .46288755780560664, (9, 1) = .4985566327609869, (9, 2) = 0.37313069594910674e-1, (9, 3) = -.10159768333703968, (9, 4) = -.2329675184040786, (9, 5) = .4045501164402566, (10, 1) = .504526521398875, (10, 2) = 0.20382679676615986e-1, (10, 3) = -0.606567047794537e-1, (10, 4) = -.1557809847294323, (10, 5) = .32029763938349964, (11, 1) = .5077218117791161, (11, 2) = 0.10501648422412073e-1, (11, 3) = -0.3401535257794869e-1, (11, 4) = -0.9702883361504151e-1, (11, 5) = .23095682422571068, (12, 1) = .5093322596657791, (12, 2) = 0.5093151483295916e-2, (12, 3) = -0.17884998462519692e-1, (12, 4) = -0.5623455808801906e-1, (12, 5) = .15225439766468124, (13, 1) = .5100955651640168, (13, 2) = 0.23195437904716377e-2, (13, 3) = -0.8800007896506692e-2, (13, 4) = -0.3029419520059991e-1, (13, 5) = 0.9199903664262538e-1, (14, 1) = .5104345698316491, (14, 2) = 0.9909285667744439e-3, (14, 3) = -0.4050636647573417e-2, (14, 4) = -0.1517584553753996e-1, (14, 5) = 0.5110208980042368e-1, (15, 1) = .5105756222550529, (15, 2) = 0.395898479049903e-3, (15, 3) = -0.17420870540071946e-2, (15, 4) = -0.70679676150117755e-2, (15, 5) = 0.2614147510937819e-1, (16, 1) = .5106303954198085, (16, 2) = 0.147062675323547e-3, (16, 3) = -0.6987853715227916e-3, (16, 4) = -0.3059943628543717e-2, (16, 5) = 0.12332878924911292e-1, (17, 1) = .5106500758344735, (17, 2) = 0.5016782526067641e-4, (17, 3) = -0.2606614231585554e-3, (17, 4) = -0.12322310129648298e-2, (17, 5) = 0.5375569850887878e-2, (18, 1) = .5106565008224614, (18, 2) = 0.15188983867428313e-4, (18, 3) = -0.8947015334152312e-4, (18, 4) = -0.4615493175592657e-3, (18, 5) = 0.21668208911118933e-2, (19, 1) = .5106582990190938, (19, 2) = 0.3766036798992976e-5, (19, 3) = -0.27659825670281336e-4, (19, 4) = -0.16295043631438081e-3, (19, 5) = 0.818490525638072e-3, (20, 1) = .5106586754129524, (20, 2) = 0.5632933568740209e-6, (20, 3) = -0.6803446974353735e-5, (20, 4) = -0.55451472121262876e-4, (20, 5) = 0.2961995690048103e-3, (21, 1) = .5106587096287567, (21, 2) = .0, (21, 3) = -.0, (21, 4) = -0.18247231920817762e-4, (21, 5) = 0.10312210298376153e-3}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(21, {(1) = .0, (2) = .19993050946471785, (3) = .40078377746315347, (4) = .6025727748609847, (5) = .805792602032412, (6) = 1.010942304650061, (7) = 1.2180763336987108, (8) = 1.4270038908463605, (9) = 1.6375902221831404, (10) = 1.8498543724186098, (11) = 2.0633079120179274, (12) = 2.277741391439103, (13) = 2.4931129139047408, (14) = 2.7089887386097495, (15) = 2.9252757828996607, (16) = 3.1419082091550377, (17) = 3.3586565343807853, (18) = 3.5755020065597023, (19) = 3.7897835066856795, (20) = 3.99778821105096, (21) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(21, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.3225282101028832e-8, (1, 4) = .0, (1, 5) = -0.306904489517561e-8, (2, 1) = 0.10246531089716523e-8, (2, 2) = -0.6348273518306401e-9, (2, 3) = 0.5280283045733476e-8, (2, 4) = -0.15460119781465505e-8, (2, 5) = -0.3111972196122568e-8, (3, 1) = 0.14385154241501163e-8, (3, 2) = -0.5659353722457318e-9, (3, 3) = 0.7366067640793483e-8, (3, 4) = -0.205675007440646e-8, (3, 5) = -0.7654892838125813e-9, (4, 1) = 0.13717815683035354e-8, (4, 2) = 0.26028484027032336e-9, (4, 3) = 0.9539892064176174e-8, (4, 4) = 0.24565765082340653e-9, (4, 5) = 0.11311960348109336e-8, (5, 1) = 0.10696619574989934e-8, (5, 2) = 0.20904757573793948e-8, (5, 3) = 0.10897034285849277e-7, (5, 4) = 0.5224442094293148e-8, (5, 5) = -0.982392164165021e-9, (6, 1) = 0.9629629242145679e-9, (6, 2) = 0.4894193344502427e-8, (6, 3) = 0.1017771761404114e-7, (6, 4) = 0.10347525459625882e-7, (6, 5) = -0.7741328730549143e-8, (7, 1) = 0.15636952892286532e-8, (7, 2) = 0.8053337086081324e-8, (7, 3) = 0.6822364946182849e-8, (7, 4) = 0.11785751490900183e-7, (7, 5) = -0.1392691114755755e-7, (8, 1) = 0.31926817803440276e-8, (8, 2) = 0.10509257498152553e-7, (8, 3) = 0.1899720513765137e-8, (8, 4) = 0.760149626720609e-8, (8, 5) = -0.11714120519495598e-7, (9, 1) = 0.57532273237297496e-8, (9, 2) = 0.11421679651998926e-7, (9, 3) = -0.229577357787563e-8, (9, 4) = 0.1716529005384147e-9, (9, 5) = 0.577665988866524e-9, (10, 1) = 0.8784212596184829e-8, (10, 2) = 0.10748645263066323e-7, (10, 3) = -0.39035239946249045e-8, (10, 4) = -0.5427240111839344e-8, (10, 5) = 0.14524777420046239e-7, (11, 1) = 0.11724890676964285e-7, (11, 2) = 0.9216439233216983e-8, (11, 3) = -0.28080368116505204e-8, (11, 4) = -0.5695308336864215e-8, (11, 5) = 0.1854188979169272e-7, (12, 1) = 0.14217506552967113e-7, (12, 2) = 0.7774557393185575e-8, (12, 3) = -0.5359664622676325e-9, (12, 4) = -0.16488517834097276e-8, (12, 5) = 0.9618376961509946e-8, (13, 1) = 0.1621520132087811e-7, (13, 2) = 0.6981599823947951e-8, (13, 3) = 0.11981824806623278e-8, (13, 4) = 0.28334363730160277e-8, (13, 5) = -0.4254474884966903e-8, (14, 1) = 0.17871713577039598e-7, (14, 2) = 0.685266473073148e-8, (14, 3) = 0.16436559065185234e-8, (14, 4) = 0.466176272654239e-8, (14, 5) = -0.12433461653275879e-7, (15, 1) = 0.19390903474282444e-7, (15, 2) = 0.7074088998861169e-8, (15, 3) = 0.11396175692924493e-8, (15, 4) = 0.36232530669465204e-8, (15, 5) = -0.11136510116613177e-7, (16, 1) = 0.20906983042953743e-7, (16, 2) = 0.7336969978980538e-8, (16, 3) = 0.4082968956704066e-9, (16, 4) = 0.14447508719698394e-8, (16, 5) = -0.441131553891032e-8, (17, 1) = 0.2246622279696012e-7, (17, 2) = 0.7494765673871917e-8, (17, 3) = -0.713044618217475e-10, (17, 4) = -0.20531471924327354e-9, (17, 5) = 0.16033357726866474e-8, (18, 1) = 0.24064316105687922e-7, (18, 2) = 0.7543231622589056e-8, (18, 3) = -0.2150775594089281e-9, (18, 4) = -0.7638272588382362e-9, (18, 5) = 0.37681131369972575e-8, (19, 1) = 0.25662794710206375e-7, (19, 2) = 0.7533978157568794e-8, (19, 3) = -0.16368473302264987e-9, (19, 4) = -0.5918687948851731e-9, (19, 5) = 0.28309099745660008e-8, (20, 1) = 0.2721985098806705e-7, (20, 2) = 0.7512291952428403e-8, (20, 3) = -0.6699548282956056e-10, (20, 4) = -0.22995298592357275e-9, (20, 5) = 0.899471197799444e-9, (21, 1) = 0.28733061733775093e-7, (21, 2) = 0.7499038130831793e-8, (21, 3) = .0, (21, 4) = .0, (21, 5) = -0.42801008501024594e-9}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[21] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(2.8733061733775093e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 21, [f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[21] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[21] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(21, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(21, 5, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), eta)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[21] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(2.8733061733775093e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 21, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[21] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[21] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(21, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(21, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(0..0, {}), (3) = [eta, f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [eta = res[1], seq('[f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), eta)]'[i] = res[i+1], i = 1 .. 5)] catch: error  end try end proc

(1)

S1(0)

[eta = 0., f[0](eta) = HFloat(0.0), diff(f[0](eta), eta) = HFloat(0.0), diff(diff(f[0](eta), eta), eta) = HFloat(0.8245101724754578), theta[0](eta) = HFloat(1.0), diff(theta[0](eta), eta) = HFloat(-0.7109880345825436)]

(2)

S1(inf)

[eta = 4.2, f[0](eta) = HFloat(1.8837944558979445), diff(f[0](eta), eta) = HFloat(0.5106587096287566), diff(diff(f[0](eta), eta), eta) = HFloat(0.0), theta[0](eta) = HFloat(0.0), diff(theta[0](eta), eta) = HFloat(-1.824723192081776e-5)]

(3)

NULL

a := 1.88379445589794-.510658709628757*inf

-.260972124

(4)

inf := 10

NULL

equ3 := diff(F[0](xi), `$`(xi, 3))+3*F[0](xi)*(diff(F[0](xi), `$`(xi, 2)))-2*(diff(F[0](xi), xi))^2

diff(diff(diff(F[0](xi), xi), xi), xi)+3*F[0](xi)*(diff(diff(F[0](xi), xi), xi))-2*(diff(F[0](xi), xi))^2

(5)

Bcs11 := F[0](0) = 0, (D(F[0]))(0) = .510618751345326, (D(F[0]))(inf) = 0

F[0](0) = 0, (D(F[0]))(0) = .510618751345326, (D(F[0]))(10) = 0

(6)

S11 := dsolve({Bcs11, equ3}, {F[0](xi)}, type = numeric)

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(23, {(1) = .0, (2) = .43995910756952955, (3) = .8818024979495411, (4) = 1.3270776004308045, (5) = 1.7763484441069568, (6) = 2.229065879136695, (7) = 2.684207128805122, (8) = 3.140817181526158, (9) = 3.5981979167878757, (10) = 4.0559771665647775, (11) = 4.513960436412507, (12) = 4.972035001116527, (13) = 5.430146736418387, (14) = 5.8882754726647875, (15) = 6.346417081862801, (16) = 6.804565947859982, (17) = 7.262708179327477, (18) = 7.720830795175491, (19) = 8.178943307293594, (20) = 8.637079917616942, (21) = 9.095271573062485, (22) = 9.55312550836552, (23) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(23, 3, {(1, 1) = .0, (1, 2) = .510618751345326, (1, 3) = -.5621776449624967, (2, 1) = .17717334220528227, (2, 2) = .3094384103457518, (2, 3) = -.36249778610993466, (3, 1) = .2835457506232679, (3, 2) = .18237603524747753, (3, 3) = -.22215239106093324, (4, 1) = .34609337288531195, (4, 2) = .10528549733875404, (4, 3) = -.1313037143718732, (5, 1) = .38226110558181875, (5, 2) = 0.5986757437392236e-1, (5, 3) = -0.7570052587025905e-1, (6, 1) = .4028817239785081, (6, 2) = 0.3368972489103516e-1, (6, 3) = -0.4293950636267703e-1, (7, 1) = .41451120840782213, (7, 2) = 0.1883373920486776e-1, (7, 3) = -0.24113598781561642e-1, (8, 1) = .4210213973431861, (8, 2) = 0.10487755429959987e-1, (8, 3) = -0.13462644018507802e-1, (9, 1) = .42464905330360847, (9, 2) = 0.5827609213592593e-2, (9, 3) = -0.7492027740321948e-2, (10, 1) = .42666537431298196, (10, 2) = 0.32341752319787276e-2, (10, 3) = -0.41620140393042165e-2, (11, 1) = .42778447655676605, (11, 2) = 0.17934853870152092e-2, (11, 3) = -0.2309891932194095e-2, (12, 1) = .42840502007546755, (12, 2) = 0.9939485823390328e-3, (12, 3) = -0.128132977545255e-2, (13, 1) = .42874885053352857, (13, 2) = 0.5504549692948659e-3, (13, 3) = -0.710585328691742e-3, (14, 1) = .428939188910442, (14, 2) = 0.3045149657496893e-3, (14, 3) = -0.3940128086348384e-3, (15, 1) = .42904440886986595, (15, 2) = 0.16814506760643266e-3, (15, 3) = -0.2184582751864434e-3, (16, 1) = .42910243164507306, (16, 2) = 0.9253589387088047e-4, (16, 3) = -0.12111740438283116e-3, (17, 1) = .4291342856498462, (17, 2) = 0.5061752912533847e-4, (17, 3) = -0.6714895745960031e-4, (18, 1) = .4291516313607923, (18, 2) = 0.27378292595049353e-4, (18, 3) = -0.37228690528137976e-4, (19, 1) = .4291609342033263, (19, 2) = 0.14494226764390213e-4, (19, 3) = -0.20640432198220086e-4, (20, 1) = .42916577833108405, (20, 2) = 0.7350727087129666e-5, (20, 3) = -0.11443117153602244e-4, (21, 1) = .42916815033963046, (21, 2) = 0.3389993912843161e-5, (21, 3) = -0.6343627852532419e-5, (22, 1) = .4291691510446365, (22, 2) = 0.11954976052799754e-5, (22, 3) = -0.35181854688677843e-5, (23, 1) = .4291693927115069, (23, 2) = .0, (23, 3) = -0.1978965807811915e-5}, datatype = float[8], order = C_order); YP := Matrix(23, 3, {(1, 1) = .510618751345326, (1, 2) = -.5621776449624967, (1, 3) = .5214630184509197, (2, 1) = .3094384103457518, (2, 2) = -.36249778610993466, (2, 3) = .3841790925159498, (3, 1) = .18237603524747753, (3, 2) = -.22215239106093324, (3, 3) = .25549313589355654, (4, 1) = .10528549733875404, (4, 2) = -.1313037143718732, (4, 3) = .15850010803773118, (5, 1) = 0.5986757437392236e-1, (5, 2) = -0.7570052587025905e-1, (5, 3) = 0.9398035305970513e-1, (6, 1) = 0.3368972489103516e-1, (6, 2) = -0.4293950636267703e-1, (6, 3) = 0.5416862217701158e-1, (7, 1) = 0.1883373920486776e-1, (7, 2) = -0.24113598781561642e-1, (7, 3) = 0.3069549037489346e-1, (8, 1) = 0.10487755429959987e-1, (8, 2) = -0.13462644018507802e-1, (8, 3) = 0.17224169617735433e-1, (9, 1) = 0.5827609213592593e-2, (9, 2) = -0.7492027740321948e-2, (9, 3) = 0.9612369520048963e-2, (10, 1) = 0.32341752319787276e-2, (10, 2) = -0.41620140393042165e-2, (10, 3) = 0.5348281612789148e-2, (11, 1) = 0.17934853870152092e-2, (11, 2) = -0.2309891932194095e-2, (11, 3) = 0.29708409130159183e-2, (12, 1) = 0.9939485823390328e-3, (12, 2) = -0.128132977545255e-2, (12, 3) = 0.16487601920967994e-2, (13, 1) = 0.5504549692948659e-3, (13, 2) = -0.710585328691742e-3, (13, 3) = 0.9145939299941647e-3, (14, 1) = 0.3045149657496893e-3, (14, 2) = -0.3940128086348384e-3, (14, 3) = 0.5072080623971895e-3, (15, 1) = 0.16814506760643266e-3, (15, 2) = -0.2184582751864434e-3, (15, 3) = 0.2812414501478151e-3, (16, 1) = 0.9253589387088047e-4, (16, 2) = -0.12111740438283116e-3, (16, 3) = 0.15593244398894642e-3, (17, 1) = 0.5061752912533847e-4, (17, 2) = -0.6714895745960031e-4, (17, 3) = 0.8645288394318198e-4, (18, 1) = 0.27378292595049353e-4, (18, 2) = -0.37228690528137976e-4, (18, 3) = 0.47931758962540315e-4, (19, 1) = 0.14494226764390213e-4, (19, 2) = -0.20640432198220086e-4, (19, 3) = 0.26574621658864638e-4, (20, 1) = 0.7350727087129666e-5, (20, 2) = -0.11443117153602244e-4, (20, 3) = 0.14733090905655878e-4, (21, 1) = 0.3389993912843161e-5, (21, 2) = -0.6343627852532419e-5, (21, 3) = 0.8167472079860358e-5, (22, 1) = 0.11954976052799754e-5, (22, 2) = -0.35181854688677843e-5, (22, 3) = 0.4529692871103739e-5, (23, 1) = .0, (23, 2) = -0.1978965807811915e-5, (23, 3) = 0.25479346618064288e-5}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(23, {(1) = .0, (2) = .43995910756952955, (3) = .8818024979495411, (4) = 1.3270776004308045, (5) = 1.7763484441069568, (6) = 2.229065879136695, (7) = 2.684207128805122, (8) = 3.140817181526158, (9) = 3.5981979167878757, (10) = 4.0559771665647775, (11) = 4.513960436412507, (12) = 4.972035001116527, (13) = 5.430146736418387, (14) = 5.8882754726647875, (15) = 6.346417081862801, (16) = 6.804565947859982, (17) = 7.262708179327477, (18) = 7.720830795175491, (19) = 8.178943307293594, (20) = 8.637079917616942, (21) = 9.095271573062485, (22) = 9.55312550836552, (23) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(23, 3, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.8443585204955963e-7, (2, 1) = 0.8072589267659636e-7, (2, 2) = -0.13040637822613006e-6, (2, 3) = 0.15281918615445138e-6, (3, 1) = 0.39989750781142555e-7, (3, 2) = -0.11177533439806323e-6, (3, 3) = 0.1352441905854288e-6, (4, 1) = -0.20600025919174704e-7, (4, 2) = -0.3663790652273445e-7, (4, 3) = 0.3961571511177524e-7, (5, 1) = -0.49196188461498834e-7, (5, 2) = 0.5492226766989574e-8, (5, 3) = -0.1811804632665225e-7, (6, 1) = -0.5176128689580457e-7, (6, 2) = 0.10746044825613138e-7, (6, 3) = -0.24261078473670985e-7, (7, 1) = -0.4605856538385761e-7, (7, 2) = 0.2347487092667642e-8, (7, 3) = -0.10120809582466025e-7, (8, 1) = -0.4167885627474688e-7, (8, 2) = -0.50636120787681426e-8, (8, 3) = 0.2710185594404049e-8, (9, 1) = -0.4055994520021322e-7, (9, 2) = -0.7884739911451825e-8, (9, 3) = 0.8563777546638327e-8, (10, 1) = -0.41605931611661884e-7, (10, 2) = -0.7347948086520706e-8, (10, 3) = 0.908101908275086e-8, (11, 1) = -0.43422115575092884e-7, (11, 2) = -0.5397359425838763e-8, (11, 3) = 0.7106596371627789e-8, (12, 1) = -0.45148718532454525e-7, (12, 2) = -0.33200029720200515e-8, (12, 3) = 0.45977051212970705e-8, (13, 1) = -0.4644624587319399e-7, (13, 2) = -0.16812844515373377e-8, (13, 3) = 0.2476976139544679e-8, (14, 1) = -0.4728162048888603e-7, (14, 2) = -0.597980012160218e-9, (14, 3) = 0.10035287537696905e-8, (15, 1) = -0.4774964466124897e-7, (15, 2) = 0.1516792967540915e-10, (15, 3) = 0.1216447480458187e-9, (16, 1) = -0.4797098512847073e-7, (16, 2) = 0.2984480082832177e-9, (16, 3) = -0.32609332485037004e-9, (17, 1) = -0.4804804671209328e-7, (17, 2) = 0.3798012127372219e-9, (17, 3) = -0.497031217110049e-9, (18, 1) = -0.4805324175520197e-7, (18, 2) = 0.3535479474474593e-9, (18, 3) = -0.5125103792466736e-9, (19, 1) = -0.48031643002679316e-7, (19, 2) = 0.28054921031195175e-9, (19, 3) = -0.4535792419789312e-9, (20, 1) = -0.4800808931165307e-7, (20, 2) = 0.19581304022615792e-9, (20, 3) = -0.3686139862436758e-9, (21, 1) = -0.4799424116835274e-7, (21, 2) = 0.11696392107492342e-9, (21, 3) = -0.2833008145543955e-9, (22, 1) = -0.4799400195331907e-7, (22, 2) = 0.51123446927522176e-10, (22, 3) = -0.20919618553471444e-9, (23, 1) = -0.4800625077534693e-7, (23, 2) = .0, (23, 3) = -0.15020239214744807e-9}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[23] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(1.5281918615445138e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [3, 23, [F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(3, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(23, 3, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(3, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(23, 3, X, Y, outpoint, yout, L, V) end if; [xi = outpoint, seq('[F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)]'[i] = yout[i], i = 1 .. 3)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[23] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(1.5281918615445138e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [3, 23, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(23, 3, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(3, {(1) = 0., (2) = 0., (3) = 0.}); `dsolve/numeric/hermite`(23, 3, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 3)] end proc, (2) = Array(0..0, {}), (3) = [xi, F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [xi = res[1], seq('[F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)]'[i] = res[i+1], i = 1 .. 3)] catch: error  end try end proc

(7)

S11(0)

[xi = 0., F[0](xi) = HFloat(0.0), diff(F[0](xi), xi) = HFloat(0.5106187513453263), diff(diff(F[0](xi), xi), xi) = HFloat(-0.562177644962497)]

(8)

S11(inf)

[xi = 10., F[0](xi) = HFloat(0.42916939271150717), diff(F[0](xi), xi) = HFloat(0.0), diff(diff(F[0](xi), xi), xi) = HFloat(-1.9789658078119164e-6)]

(9)

NULL

NULL

inf := 4.2

equ4 := diff(f[1](eta), `$`(eta, 3))+theta[1](eta) = 0

equ5 := diff(theta[1](eta), `$`(eta, 2))+(3*1.88379445589794)*(diff(theta[1](eta), eta))+(3*(-0.182472319208178e-4))*f[1](eta) = 0

Bcs2 := f[1](0) = 0, (D(f[1]))(0) = 0, theta[1](0) = 0, theta[1](inf) = 0, (D(D(f[1])))(inf) = -.562177644962497

S2 := dsolve({Bcs2, equ4, equ5}, {f[1](eta), theta[1](eta)}, type = numeric)

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(11, {(1) = .0, (2) = .4116634332886109, (3) = .8886010476858462, (4) = 1.3528488149076092, (5) = 1.8045807366238487, (6) = 2.241555102796764, (7) = 2.6625695592004965, (8) = 3.0672725690885674, (9) = 3.4556665515316527, (10) = 3.831324258983187, (11) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(11, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -.5619986895834216, (1, 4) = .0, (1, 5) = 0.335774149965343e-3, (2, 1) = -0.4762032358997575e-1, (2, 2) = -.23135669488800123, (2, 3) = -.5620136602440209, (2, 4) = 0.53584183105081106e-4, (2, 5) = 0.3259167905984578e-4, (3, 1) = -.22188452637683598, (3, 2) = -.49940857560864915, (3, 3) = -.5620409665524415, (3, 4) = 0.58646668768565734e-4, (3, 5) = 0.7416150484543588e-6, (4, 1) = -.5143020373634434, (4, 2) = -.7603411477852857, (4, 3) = -.5620680774630706, (4, 4) = 0.5782030426624352e-4, (4, 5) = -0.3686352453447587e-5, (5, 1) = -.9151215778516861, (5, 2) = -1.0142510703826526, (5, 3) = -.5620937045204393, (5, 4) = 0.55371378860239725e-4, (5, 5) = -0.72839758029738255e-5, (6, 1) = -1.41198899414111, (6, 2) = -1.2598767815850975, (6, 3) = -.5621170728942686, (6, 4) = 0.51263362070545665e-4, (6, 5) = -0.11687120529486582e-4, (7, 1) = -1.9922344707360793, (7, 2) = -1.4965405780807717, (7, 3) = -.5621374727450006, (7, 4) = 0.4527873193435496e-4, (7, 5) = -0.16902962326608247e-4, (8, 1) = -2.643924136984444, (8, 2) = -1.7240428108976953, (8, 3) = -.5621542573727711, (8, 4) = 0.3726965687176117e-4, (8, 5) = -0.22825657629343497e-4, (9, 1) = -3.3559327840238864, (9, 2) = -1.9423827145168133, (9, 3) = -.5621668522332793, (9, 4) = 0.2716422553072306e-4, (9, 5) = -0.29348255430226227e-4, (10, 1) = -4.125270167459166, (10, 2) = -2.1535666676671648, (10, 3) = -.5621748236492027, (10, 4) = 0.14831645690104376e-4, (10, 5) = -0.3643841995320963e-4, (11, 1) = -4.957443956702882, (11, 2) = -2.3608275753757364, (11, 3) = -.562177644962497, (11, 4) = .0, (11, 5) = -0.4414396637606905e-4}, datatype = float[8], order = C_order); YP := Matrix(11, 5, {(1, 1) = .0, (1, 2) = -.5619986895834216, (1, 3) = -.0, (1, 4) = 0.335774149965343e-3, (1, 5) = -0.18975884465184773e-2, (2, 1) = -.23135669488800123, (2, 2) = -.5620136602440209, (2, 3) = -0.53584183105081106e-4, (2, 4) = 0.3259167905984578e-4, (2, 5) = -0.18679489023996156e-3, (3, 1) = -.49940857560864915, (3, 2) = -.5620409665524415, (3, 3) = -0.58646668768565734e-4, (3, 4) = 0.7416150484543588e-6, (3, 5) = -0.16337486187065928e-4, (4, 1) = -.7603411477852857, (4, 2) = -.5620680774630706, (4, 3) = -0.5782030426624352e-4, (4, 4) = -0.3686352453447587e-5, (4, 5) = -0.732077471409808e-5, (5, 1) = -1.0142510703826526, (5, 2) = -.5620937045204393, (5, 3) = -0.55371378860239725e-4, (5, 4) = -0.72839758029738255e-5, (5, 5) = -0.893076729232743e-5, (6, 1) = -1.2598767815850975, (6, 2) = -.5621170728942686, (6, 3) = -0.51263362070545665e-4, (6, 4) = -0.11687120529486582e-4, (6, 5) = -0.11246273353589229e-4, (7, 1) = -1.4965405780807717, (7, 2) = -.5621374727450006, (7, 3) = -0.4527873193435496e-4, (7, 4) = -0.16902962326608247e-4, (7, 5) = -0.13533173117094628e-4, (8, 1) = -1.7240428108976953, (8, 2) = -.5621542573727711, (8, 3) = -0.3726965687176117e-4, (8, 4) = -0.22825657629343497e-4, (8, 5) = -0.1573634882918884e-4, (9, 1) = -1.9423827145168133, (9, 2) = -.5621668522332793, (9, 3) = -0.2716422553072306e-4, (9, 4) = -0.29348255430226227e-4, (9, 5) = -0.17851208835849183e-4, (10, 1) = -2.1535666676671648, (10, 2) = -.5621748236492027, (10, 3) = -0.14831645690104376e-4, (10, 4) = -0.3643841995320963e-4, (10, 5) = -0.1989680395508565e-4, (11, 1) = -2.3608275753757364, (11, 2) = -.562177644962497, (11, 3) = -.0, (11, 4) = -0.4414396637606905e-4, (11, 5) = -0.2190441144981183e-4}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(11, {(1) = .0, (2) = .4116634332886109, (3) = .8886010476858462, (4) = 1.3528488149076092, (5) = 1.8045807366238487, (6) = 2.241555102796764, (7) = 2.6625695592004965, (8) = 3.0672725690885674, (9) = 3.4556665515316527, (10) = 3.831324258983187, (11) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(11, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.35508604778067024e-15, (1, 4) = .0, (1, 5) = 0.15397753328418554e-14, (2, 1) = 0.2558116197637096e-10, (2, 2) = -0.14456757081707498e-9, (2, 3) = 0.817011120093731e-9, (2, 4) = 0.4617236684306891e-8, (2, 5) = -0.2609377331174807e-7, (3, 1) = -0.9457936005633856e-11, (3, 2) = 0.5345381823058202e-10, (3, 3) = -0.30207991081338217e-9, (3, 4) = -0.1707174526030626e-8, (3, 5) = 0.9647899354096491e-8, (4, 1) = 0.2020346996825016e-11, (4, 2) = -0.11415519234215377e-10, (4, 3) = 0.6451847526201498e-10, (4, 4) = 0.3646134887612831e-9, (4, 5) = -0.2060569086207772e-8, (5, 1) = -0.17646929046515701e-12, (5, 2) = 0.10093169744755152e-11, (5, 3) = -0.5699389218375125e-11, (5, 4) = -0.3221591809328718e-10, (5, 5) = 0.18206604502968212e-9, (6, 1) = 0.8757302096159674e-14, (6, 2) = -0.3799530988879617e-13, (6, 3) = 0.2292287437287893e-12, (6, 4) = 0.12945323288954797e-11, (6, 5) = -0.731435866077949e-11, (7, 1) = -0.9110226200220738e-15, (7, 2) = 0.25567726327308368e-13, (7, 3) = -0.12993934244362953e-12, (7, 4) = -0.7335757077118738e-12, (7, 5) = 0.4147257410839353e-11, (8, 1) = 0.26358911697616852e-14, (8, 2) = 0.3882634055360638e-14, (8, 3) = -0.9480934215017551e-14, (8, 4) = -0.55231163150641485e-13, (8, 5) = 0.31367270612471335e-12, (9, 1) = 0.7629602722383346e-14, (9, 2) = 0.4396554488606655e-14, (9, 3) = -0.15992210754706523e-14, (9, 4) = -0.1230013855036495e-13, (9, 5) = 0.7105291182052132e-13, (10, 1) = 0.1485070353377911e-13, (10, 2) = 0.33969966675655985e-14, (10, 3) = -0.6675463903849193e-15, (10, 4) = -0.14924562287319862e-14, (10, 5) = 0.9974730177955179e-14, (11, 1) = 0.38908323477587536e-14, (11, 2) = 0.32750628566257692e-14, (11, 3) = .0, (11, 4) = .0, (11, 5) = 0.15404022343639915e-14}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[11] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.609377331174807e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 11, [f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[11] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[11] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(11, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(11, 5, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), eta)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[11] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.609377331174807e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 11, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[11] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[11] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(11, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(11, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(0..0, {}), (3) = [eta, f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [eta = res[1], seq('[f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), eta)]'[i] = res[i+1], i = 1 .. 5)] catch: error  end try end proc

(10)

S2(0)

[eta = 0., f[1](eta) = HFloat(0.0), diff(f[1](eta), eta) = HFloat(0.0), diff(diff(f[1](eta), eta), eta) = HFloat(-0.5619986895834218), theta[1](eta) = HFloat(0.0), diff(theta[1](eta), eta) = HFloat(3.3577414996534315e-4)]

(11)

S2(inf)

[eta = 4.2, f[1](eta) = HFloat(-4.95744395670288), diff(f[1](eta), eta) = HFloat(-2.3608275753757355), diff(diff(f[1](eta), eta), eta) = HFloat(-0.5621776449624968), theta[1](eta) = HFloat(0.0), diff(theta[1](eta), eta) = HFloat(-4.414396637606903e-5)]

(12)

"b:="

inf := 10

equ6 := diff(F[1](xi), `$`(xi, 3))-(4*.510618751345326)*(diff(F[1](xi), xi))+(3*(-.562177644962497))*F[1](0) = 0

diff(diff(diff(F[1](xi), xi), xi), xi)-2.042475005*(diff(F[1](xi), xi))-1.686532935*F[1](0) = 0

(13)

Bcs21 := F[1](0) = a, (D(F[1]))(0) = .510658709628757, (D(F[1]))(inf) = 0

F[1](0) = -.260972124, (D(F[1]))(0) = .510658709628757, (D(F[1]))(10) = 0

(14)

S21 := dsolve({Bcs21, equ6}, {F[1](xi)}, type = numeric)

Error, (in fproc) unable to store 'HFloat(1.0430076505022892)+1.686532935*F[1](0)' when datatype=float[8]

 

NULL

NULL


 

Download kuikennnnnn.mw
 

NULL

restart

Digits := 10

with(ODETools)

with(student)

with(plots)

inf := 4.2

NULL

equ1 := diff(f[0](eta), `$`(eta, 3))+theta[0](eta) = 0

equ2 := diff(theta[0](eta), `$`(eta, 2))+3*f[0](eta)*(diff(theta[0](eta), eta)) = 0

Bcs1 := f[0](0) = 0, (D(f[0]))(0) = 0, theta[0](0) = 1, theta[0](inf) = 0, (D(D(f[0])))(inf) = 0

S1 := dsolve({Bcs1, equ1, equ2}, {f[0](eta), theta[0](eta)}, type = numeric)

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(21, {(1) = .0, (2) = .19993050946471785, (3) = .40078377746315347, (4) = .6025727748609847, (5) = .805792602032412, (6) = 1.010942304650061, (7) = 1.2180763336987108, (8) = 1.4270038908463605, (9) = 1.6375902221831404, (10) = 1.8498543724186098, (11) = 2.0633079120179274, (12) = 2.277741391439103, (13) = 2.4931129139047408, (14) = 2.7089887386097495, (15) = 2.9252757828996607, (16) = 3.1419082091550377, (17) = 3.3586565343807853, (18) = 3.5755020065597023, (19) = 3.7897835066856795, (20) = 3.99778821105096, (21) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(21, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .8245101724754578, (1, 4) = 1.0, (1, 5) = -.7109880345825436, (2, 1) = 0.15194130384185354e-1, (2, 2) = .14580548143397778, (2, 3) = .6387850483082825, (2, 4) = .857963238913636, (2, 5) = -.7087869877011237, (3, 1) = 0.5625387147295941e-1, (3, 2) = .2577556073775664, (3, 3) = .4806893773780191, (3, 4) = .7167515674300292, (3, 5) = -.6944757971749999, (4, 1) = .11711872046127954, (4, 2) = .34110224456170846, (4, 3) = .3499979513587831, (4, 4) = .5797495081496531, (4, 5) = -.6595302165926753, (5, 1) = .19289982468547776, (5, 2) = .4011617938545637, (5, 3) = .24543411078038904, (5, 4) = .4513251759894287, (5, 5) = -.6004288125540566, (6, 1) = .2797565188640971, (6, 2) = .4428520778243424, (6, 3) = .16494373679100188, (6, 4) = .3361497197458259, (6, 5) = -.5193790217421129, (7, 1) = .37456519619918616, (7, 2) = .4705413231882741, (7, 3) = .10579089990103963, (7, 4) = .23830615973840436, (7, 5) = -.4239568572171149, (8, 1) = .4748530263492926, (8, 2) = .48804935564305746, (8, 3) = 0.6453023961994517e-1, (8, 4) = .16012402142182885, (8, 5) = -.3249339143694787, (9, 1) = .5788362246256302, (9, 2) = .4985566327609869, (9, 3) = 0.37313069594910674e-1, (9, 4) = .10159768333703968, (9, 5) = -.2329675184040786, (10, 1) = .6853588708527928, (10, 2) = .504526521398875, (10, 3) = 0.20382679676615986e-1, (10, 4) = 0.606567047794537e-1, (10, 5) = -.1557809847294323, (11, 1) = .7934302125147107, (11, 2) = .5077218117791161, (11, 3) = 0.10501648422412073e-1, (11, 4) = 0.3401535257794869e-1, (11, 5) = -0.9702883361504151e-1, (12, 1) = .9024960382686785, (12, 2) = .5093322596657791, (12, 3) = 0.5093151483295916e-2, (12, 4) = 0.17884998462519692e-1, (12, 5) = -0.5623455808801906e-1, (13, 1) = 1.012284543110573, (13, 2) = .5100955651640168, (13, 3) = 0.23195437904716377e-2, (13, 4) = 0.8800007896506692e-2, (13, 5) = -0.3029419520059991e-1, (14, 1) = 1.1224435496090202, (14, 2) = .5104345698316491, (14, 3) = 0.9909285667744439e-3, (14, 4) = 0.4050636647573417e-2, (14, 5) = -0.1517584553753996e-1, (15, 1) = 1.2328614831160174, (15, 2) = .5105756222550529, (15, 3) = 0.395898479049903e-3, (15, 4) = 0.17420870540071946e-2, (15, 5) = -0.70679676150117755e-2, (16, 1) = 1.3434756128476715, (16, 2) = .5106303954198085, (16, 3) = 0.147062675323547e-3, (16, 4) = 0.6987853715227916e-3, (16, 5) = -0.3059943628543717e-2, (17, 1) = 1.4541564025817688, (17, 2) = .5106500758344735, (17, 3) = 0.5016782526067641e-4, (17, 4) = 0.2606614231585554e-3, (17, 5) = -0.12322310129648298e-2, (18, 1) = 1.5648893907808388, (18, 2) = .5106565008224614, (18, 3) = 0.15188983867428313e-4, (18, 4) = 0.8947015334152312e-4, (18, 5) = -0.4615493175592657e-3, (19, 1) = 1.6743138673548472, (19, 2) = .5106582990190938, (19, 3) = 0.3766036798992976e-5, (19, 4) = 0.27659825670281336e-4, (19, 5) = -0.16295043631438081e-3, (20, 1) = 1.780533246301514, (20, 2) = .5106586754129524, (20, 3) = 0.5632933568740209e-6, (20, 4) = 0.6803446974353735e-5, (20, 5) = -0.55451472121262876e-4, (21, 1) = 1.883794455897945, (21, 2) = .5106587096287567, (21, 3) = .0, (21, 4) = .0, (21, 5) = -0.18247231920817762e-4}, datatype = float[8], order = C_order); YP := Matrix(21, 5, {(1, 1) = .0, (1, 2) = .8245101724754578, (1, 3) = -1.0, (1, 4) = -.7109880345825436, (1, 5) = .0, (2, 1) = .14580548143397778, (2, 2) = .6387850483082825, (2, 3) = -.857963238913636, (2, 4) = -.7087869877011237, (2, 5) = 0.3230820571723456e-1, (3, 1) = .2577556073775664, (3, 2) = .4806893773780191, (3, 3) = -.7167515674300292, (3, 4) = -.6944757971749999, (3, 5) = .11720085670609043, (4, 1) = .34110224456170846, (4, 2) = .3499979513587831, (4, 3) = -.5797495081496531, (4, 4) = -.6595302165926753, (4, 5) = .23173000521865406, (5, 1) = .4011617938545637, (5, 2) = .24543411078038904, (5, 3) = -.4513251759894287, (5, 4) = -.6004288125540566, (5, 5) = .3474678380333613, (6, 1) = .4428520778243424, (6, 2) = .16494373679100188, (6, 3) = -.3361497197458259, (6, 4) = -.5193790217421129, (6, 5) = .4358990012808411, (7, 1) = .4705413231882741, (7, 2) = .10579089990103963, (7, 3) = -.23830615973840436, (7, 4) = -.4239568572171149, (7, 5) = .47639845021055693, (8, 1) = .48804935564305746, (8, 2) = 0.6453023961994517e-1, (8, 3) = -.16012402142182885, (8, 4) = -.3249339143694787, (8, 5) = .46288755780560664, (9, 1) = .4985566327609869, (9, 2) = 0.37313069594910674e-1, (9, 3) = -.10159768333703968, (9, 4) = -.2329675184040786, (9, 5) = .4045501164402566, (10, 1) = .504526521398875, (10, 2) = 0.20382679676615986e-1, (10, 3) = -0.606567047794537e-1, (10, 4) = -.1557809847294323, (10, 5) = .32029763938349964, (11, 1) = .5077218117791161, (11, 2) = 0.10501648422412073e-1, (11, 3) = -0.3401535257794869e-1, (11, 4) = -0.9702883361504151e-1, (11, 5) = .23095682422571068, (12, 1) = .5093322596657791, (12, 2) = 0.5093151483295916e-2, (12, 3) = -0.17884998462519692e-1, (12, 4) = -0.5623455808801906e-1, (12, 5) = .15225439766468124, (13, 1) = .5100955651640168, (13, 2) = 0.23195437904716377e-2, (13, 3) = -0.8800007896506692e-2, (13, 4) = -0.3029419520059991e-1, (13, 5) = 0.9199903664262538e-1, (14, 1) = .5104345698316491, (14, 2) = 0.9909285667744439e-3, (14, 3) = -0.4050636647573417e-2, (14, 4) = -0.1517584553753996e-1, (14, 5) = 0.5110208980042368e-1, (15, 1) = .5105756222550529, (15, 2) = 0.395898479049903e-3, (15, 3) = -0.17420870540071946e-2, (15, 4) = -0.70679676150117755e-2, (15, 5) = 0.2614147510937819e-1, (16, 1) = .5106303954198085, (16, 2) = 0.147062675323547e-3, (16, 3) = -0.6987853715227916e-3, (16, 4) = -0.3059943628543717e-2, (16, 5) = 0.12332878924911292e-1, (17, 1) = .5106500758344735, (17, 2) = 0.5016782526067641e-4, (17, 3) = -0.2606614231585554e-3, (17, 4) = -0.12322310129648298e-2, (17, 5) = 0.5375569850887878e-2, (18, 1) = .5106565008224614, (18, 2) = 0.15188983867428313e-4, (18, 3) = -0.8947015334152312e-4, (18, 4) = -0.4615493175592657e-3, (18, 5) = 0.21668208911118933e-2, (19, 1) = .5106582990190938, (19, 2) = 0.3766036798992976e-5, (19, 3) = -0.27659825670281336e-4, (19, 4) = -0.16295043631438081e-3, (19, 5) = 0.818490525638072e-3, (20, 1) = .5106586754129524, (20, 2) = 0.5632933568740209e-6, (20, 3) = -0.6803446974353735e-5, (20, 4) = -0.55451472121262876e-4, (20, 5) = 0.2961995690048103e-3, (21, 1) = .5106587096287567, (21, 2) = .0, (21, 3) = -.0, (21, 4) = -0.18247231920817762e-4, (21, 5) = 0.10312210298376153e-3}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(21, {(1) = .0, (2) = .19993050946471785, (3) = .40078377746315347, (4) = .6025727748609847, (5) = .805792602032412, (6) = 1.010942304650061, (7) = 1.2180763336987108, (8) = 1.4270038908463605, (9) = 1.6375902221831404, (10) = 1.8498543724186098, (11) = 2.0633079120179274, (12) = 2.277741391439103, (13) = 2.4931129139047408, (14) = 2.7089887386097495, (15) = 2.9252757828996607, (16) = 3.1419082091550377, (17) = 3.3586565343807853, (18) = 3.5755020065597023, (19) = 3.7897835066856795, (20) = 3.99778821105096, (21) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(21, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.3225282101028832e-8, (1, 4) = .0, (1, 5) = -0.306904489517561e-8, (2, 1) = 0.10246531089716523e-8, (2, 2) = -0.6348273518306401e-9, (2, 3) = 0.5280283045733476e-8, (2, 4) = -0.15460119781465505e-8, (2, 5) = -0.3111972196122568e-8, (3, 1) = 0.14385154241501163e-8, (3, 2) = -0.5659353722457318e-9, (3, 3) = 0.7366067640793483e-8, (3, 4) = -0.205675007440646e-8, (3, 5) = -0.7654892838125813e-9, (4, 1) = 0.13717815683035354e-8, (4, 2) = 0.26028484027032336e-9, (4, 3) = 0.9539892064176174e-8, (4, 4) = 0.24565765082340653e-9, (4, 5) = 0.11311960348109336e-8, (5, 1) = 0.10696619574989934e-8, (5, 2) = 0.20904757573793948e-8, (5, 3) = 0.10897034285849277e-7, (5, 4) = 0.5224442094293148e-8, (5, 5) = -0.982392164165021e-9, (6, 1) = 0.9629629242145679e-9, (6, 2) = 0.4894193344502427e-8, (6, 3) = 0.1017771761404114e-7, (6, 4) = 0.10347525459625882e-7, (6, 5) = -0.7741328730549143e-8, (7, 1) = 0.15636952892286532e-8, (7, 2) = 0.8053337086081324e-8, (7, 3) = 0.6822364946182849e-8, (7, 4) = 0.11785751490900183e-7, (7, 5) = -0.1392691114755755e-7, (8, 1) = 0.31926817803440276e-8, (8, 2) = 0.10509257498152553e-7, (8, 3) = 0.1899720513765137e-8, (8, 4) = 0.760149626720609e-8, (8, 5) = -0.11714120519495598e-7, (9, 1) = 0.57532273237297496e-8, (9, 2) = 0.11421679651998926e-7, (9, 3) = -0.229577357787563e-8, (9, 4) = 0.1716529005384147e-9, (9, 5) = 0.577665988866524e-9, (10, 1) = 0.8784212596184829e-8, (10, 2) = 0.10748645263066323e-7, (10, 3) = -0.39035239946249045e-8, (10, 4) = -0.5427240111839344e-8, (10, 5) = 0.14524777420046239e-7, (11, 1) = 0.11724890676964285e-7, (11, 2) = 0.9216439233216983e-8, (11, 3) = -0.28080368116505204e-8, (11, 4) = -0.5695308336864215e-8, (11, 5) = 0.1854188979169272e-7, (12, 1) = 0.14217506552967113e-7, (12, 2) = 0.7774557393185575e-8, (12, 3) = -0.5359664622676325e-9, (12, 4) = -0.16488517834097276e-8, (12, 5) = 0.9618376961509946e-8, (13, 1) = 0.1621520132087811e-7, (13, 2) = 0.6981599823947951e-8, (13, 3) = 0.11981824806623278e-8, (13, 4) = 0.28334363730160277e-8, (13, 5) = -0.4254474884966903e-8, (14, 1) = 0.17871713577039598e-7, (14, 2) = 0.685266473073148e-8, (14, 3) = 0.16436559065185234e-8, (14, 4) = 0.466176272654239e-8, (14, 5) = -0.12433461653275879e-7, (15, 1) = 0.19390903474282444e-7, (15, 2) = 0.7074088998861169e-8, (15, 3) = 0.11396175692924493e-8, (15, 4) = 0.36232530669465204e-8, (15, 5) = -0.11136510116613177e-7, (16, 1) = 0.20906983042953743e-7, (16, 2) = 0.7336969978980538e-8, (16, 3) = 0.4082968956704066e-9, (16, 4) = 0.14447508719698394e-8, (16, 5) = -0.441131553891032e-8, (17, 1) = 0.2246622279696012e-7, (17, 2) = 0.7494765673871917e-8, (17, 3) = -0.713044618217475e-10, (17, 4) = -0.20531471924327354e-9, (17, 5) = 0.16033357726866474e-8, (18, 1) = 0.24064316105687922e-7, (18, 2) = 0.7543231622589056e-8, (18, 3) = -0.2150775594089281e-9, (18, 4) = -0.7638272588382362e-9, (18, 5) = 0.37681131369972575e-8, (19, 1) = 0.25662794710206375e-7, (19, 2) = 0.7533978157568794e-8, (19, 3) = -0.16368473302264987e-9, (19, 4) = -0.5918687948851731e-9, (19, 5) = 0.28309099745660008e-8, (20, 1) = 0.2721985098806705e-7, (20, 2) = 0.7512291952428403e-8, (20, 3) = -0.6699548282956056e-10, (20, 4) = -0.22995298592357275e-9, (20, 5) = 0.899471197799444e-9, (21, 1) = 0.28733061733775093e-7, (21, 2) = 0.7499038130831793e-8, (21, 3) = .0, (21, 4) = .0, (21, 5) = -0.42801008501024594e-9}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[21] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(2.8733061733775093e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 21, [f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[21] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[21] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(21, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(21, 5, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), eta)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[21] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(2.8733061733775093e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 21, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[21] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[21] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(21, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(21, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(0..0, {}), (3) = [eta, f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [eta = res[1], seq('[f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), eta)]'[i] = res[i+1], i = 1 .. 5)] catch: error  end try end proc

(1)

S1(0)

[eta = 0., f[0](eta) = HFloat(0.0), diff(f[0](eta), eta) = HFloat(0.0), diff(diff(f[0](eta), eta), eta) = HFloat(0.8245101724754578), theta[0](eta) = HFloat(1.0), diff(theta[0](eta), eta) = HFloat(-0.7109880345825436)]

(2)

S1(inf)

[eta = 4.2, f[0](eta) = HFloat(1.8837944558979445), diff(f[0](eta), eta) = HFloat(0.5106587096287566), diff(diff(f[0](eta), eta), eta) = HFloat(0.0), theta[0](eta) = HFloat(0.0), diff(theta[0](eta), eta) = HFloat(-1.824723192081776e-5)]

(3)

NULL

a := 1.88379445589794-.510658709628757*inf

-.260972124

(4)

inf := 10

NULL

equ3 := diff(F[0](xi), `$`(xi, 3))+3*F[0](xi)*(diff(F[0](xi), `$`(xi, 2)))-2*(diff(F[0](xi), xi))^2

diff(diff(diff(F[0](xi), xi), xi), xi)+3*F[0](xi)*(diff(diff(F[0](xi), xi), xi))-2*(diff(F[0](xi), xi))^2

(5)

Bcs11 := F[0](0) = 0, (D(F[0]))(0) = .510618751345326, (D(F[0]))(inf) = 0

F[0](0) = 0, (D(F[0]))(0) = .510618751345326, (D(F[0]))(10) = 0

(6)

S11 := dsolve({Bcs11, equ3}, {F[0](xi)}, type = numeric)

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(23, {(1) = .0, (2) = .43995910756952955, (3) = .8818024979495411, (4) = 1.3270776004308045, (5) = 1.7763484441069568, (6) = 2.229065879136695, (7) = 2.684207128805122, (8) = 3.140817181526158, (9) = 3.5981979167878757, (10) = 4.0559771665647775, (11) = 4.513960436412507, (12) = 4.972035001116527, (13) = 5.430146736418387, (14) = 5.8882754726647875, (15) = 6.346417081862801, (16) = 6.804565947859982, (17) = 7.262708179327477, (18) = 7.720830795175491, (19) = 8.178943307293594, (20) = 8.637079917616942, (21) = 9.095271573062485, (22) = 9.55312550836552, (23) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(23, 3, {(1, 1) = .0, (1, 2) = .510618751345326, (1, 3) = -.5621776449624967, (2, 1) = .17717334220528227, (2, 2) = .3094384103457518, (2, 3) = -.36249778610993466, (3, 1) = .2835457506232679, (3, 2) = .18237603524747753, (3, 3) = -.22215239106093324, (4, 1) = .34609337288531195, (4, 2) = .10528549733875404, (4, 3) = -.1313037143718732, (5, 1) = .38226110558181875, (5, 2) = 0.5986757437392236e-1, (5, 3) = -0.7570052587025905e-1, (6, 1) = .4028817239785081, (6, 2) = 0.3368972489103516e-1, (6, 3) = -0.4293950636267703e-1, (7, 1) = .41451120840782213, (7, 2) = 0.1883373920486776e-1, (7, 3) = -0.24113598781561642e-1, (8, 1) = .4210213973431861, (8, 2) = 0.10487755429959987e-1, (8, 3) = -0.13462644018507802e-1, (9, 1) = .42464905330360847, (9, 2) = 0.5827609213592593e-2, (9, 3) = -0.7492027740321948e-2, (10, 1) = .42666537431298196, (10, 2) = 0.32341752319787276e-2, (10, 3) = -0.41620140393042165e-2, (11, 1) = .42778447655676605, (11, 2) = 0.17934853870152092e-2, (11, 3) = -0.2309891932194095e-2, (12, 1) = .42840502007546755, (12, 2) = 0.9939485823390328e-3, (12, 3) = -0.128132977545255e-2, (13, 1) = .42874885053352857, (13, 2) = 0.5504549692948659e-3, (13, 3) = -0.710585328691742e-3, (14, 1) = .428939188910442, (14, 2) = 0.3045149657496893e-3, (14, 3) = -0.3940128086348384e-3, (15, 1) = .42904440886986595, (15, 2) = 0.16814506760643266e-3, (15, 3) = -0.2184582751864434e-3, (16, 1) = .42910243164507306, (16, 2) = 0.9253589387088047e-4, (16, 3) = -0.12111740438283116e-3, (17, 1) = .4291342856498462, (17, 2) = 0.5061752912533847e-4, (17, 3) = -0.6714895745960031e-4, (18, 1) = .4291516313607923, (18, 2) = 0.27378292595049353e-4, (18, 3) = -0.37228690528137976e-4, (19, 1) = .4291609342033263, (19, 2) = 0.14494226764390213e-4, (19, 3) = -0.20640432198220086e-4, (20, 1) = .42916577833108405, (20, 2) = 0.7350727087129666e-5, (20, 3) = -0.11443117153602244e-4, (21, 1) = .42916815033963046, (21, 2) = 0.3389993912843161e-5, (21, 3) = -0.6343627852532419e-5, (22, 1) = .4291691510446365, (22, 2) = 0.11954976052799754e-5, (22, 3) = -0.35181854688677843e-5, (23, 1) = .4291693927115069, (23, 2) = .0, (23, 3) = -0.1978965807811915e-5}, datatype = float[8], order = C_order); YP := Matrix(23, 3, {(1, 1) = .510618751345326, (1, 2) = -.5621776449624967, (1, 3) = .5214630184509197, (2, 1) = .3094384103457518, (2, 2) = -.36249778610993466, (2, 3) = .3841790925159498, (3, 1) = .18237603524747753, (3, 2) = -.22215239106093324, (3, 3) = .25549313589355654, (4, 1) = .10528549733875404, (4, 2) = -.1313037143718732, (4, 3) = .15850010803773118, (5, 1) = 0.5986757437392236e-1, (5, 2) = -0.7570052587025905e-1, (5, 3) = 0.9398035305970513e-1, (6, 1) = 0.3368972489103516e-1, (6, 2) = -0.4293950636267703e-1, (6, 3) = 0.5416862217701158e-1, (7, 1) = 0.1883373920486776e-1, (7, 2) = -0.24113598781561642e-1, (7, 3) = 0.3069549037489346e-1, (8, 1) = 0.10487755429959987e-1, (8, 2) = -0.13462644018507802e-1, (8, 3) = 0.17224169617735433e-1, (9, 1) = 0.5827609213592593e-2, (9, 2) = -0.7492027740321948e-2, (9, 3) = 0.9612369520048963e-2, (10, 1) = 0.32341752319787276e-2, (10, 2) = -0.41620140393042165e-2, (10, 3) = 0.5348281612789148e-2, (11, 1) = 0.17934853870152092e-2, (11, 2) = -0.2309891932194095e-2, (11, 3) = 0.29708409130159183e-2, (12, 1) = 0.9939485823390328e-3, (12, 2) = -0.128132977545255e-2, (12, 3) = 0.16487601920967994e-2, (13, 1) = 0.5504549692948659e-3, (13, 2) = -0.710585328691742e-3, (13, 3) = 0.9145939299941647e-3, (14, 1) = 0.3045149657496893e-3, (14, 2) = -0.3940128086348384e-3, (14, 3) = 0.5072080623971895e-3, (15, 1) = 0.16814506760643266e-3, (15, 2) = -0.2184582751864434e-3, (15, 3) = 0.2812414501478151e-3, (16, 1) = 0.9253589387088047e-4, (16, 2) = -0.12111740438283116e-3, (16, 3) = 0.15593244398894642e-3, (17, 1) = 0.5061752912533847e-4, (17, 2) = -0.6714895745960031e-4, (17, 3) = 0.8645288394318198e-4, (18, 1) = 0.27378292595049353e-4, (18, 2) = -0.37228690528137976e-4, (18, 3) = 0.47931758962540315e-4, (19, 1) = 0.14494226764390213e-4, (19, 2) = -0.20640432198220086e-4, (19, 3) = 0.26574621658864638e-4, (20, 1) = 0.7350727087129666e-5, (20, 2) = -0.11443117153602244e-4, (20, 3) = 0.14733090905655878e-4, (21, 1) = 0.3389993912843161e-5, (21, 2) = -0.6343627852532419e-5, (21, 3) = 0.8167472079860358e-5, (22, 1) = 0.11954976052799754e-5, (22, 2) = -0.35181854688677843e-5, (22, 3) = 0.4529692871103739e-5, (23, 1) = .0, (23, 2) = -0.1978965807811915e-5, (23, 3) = 0.25479346618064288e-5}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(23, {(1) = .0, (2) = .43995910756952955, (3) = .8818024979495411, (4) = 1.3270776004308045, (5) = 1.7763484441069568, (6) = 2.229065879136695, (7) = 2.684207128805122, (8) = 3.140817181526158, (9) = 3.5981979167878757, (10) = 4.0559771665647775, (11) = 4.513960436412507, (12) = 4.972035001116527, (13) = 5.430146736418387, (14) = 5.8882754726647875, (15) = 6.346417081862801, (16) = 6.804565947859982, (17) = 7.262708179327477, (18) = 7.720830795175491, (19) = 8.178943307293594, (20) = 8.637079917616942, (21) = 9.095271573062485, (22) = 9.55312550836552, (23) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(23, 3, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.8443585204955963e-7, (2, 1) = 0.8072589267659636e-7, (2, 2) = -0.13040637822613006e-6, (2, 3) = 0.15281918615445138e-6, (3, 1) = 0.39989750781142555e-7, (3, 2) = -0.11177533439806323e-6, (3, 3) = 0.1352441905854288e-6, (4, 1) = -0.20600025919174704e-7, (4, 2) = -0.3663790652273445e-7, (4, 3) = 0.3961571511177524e-7, (5, 1) = -0.49196188461498834e-7, (5, 2) = 0.5492226766989574e-8, (5, 3) = -0.1811804632665225e-7, (6, 1) = -0.5176128689580457e-7, (6, 2) = 0.10746044825613138e-7, (6, 3) = -0.24261078473670985e-7, (7, 1) = -0.4605856538385761e-7, (7, 2) = 0.2347487092667642e-8, (7, 3) = -0.10120809582466025e-7, (8, 1) = -0.4167885627474688e-7, (8, 2) = -0.50636120787681426e-8, (8, 3) = 0.2710185594404049e-8, (9, 1) = -0.4055994520021322e-7, (9, 2) = -0.7884739911451825e-8, (9, 3) = 0.8563777546638327e-8, (10, 1) = -0.41605931611661884e-7, (10, 2) = -0.7347948086520706e-8, (10, 3) = 0.908101908275086e-8, (11, 1) = -0.43422115575092884e-7, (11, 2) = -0.5397359425838763e-8, (11, 3) = 0.7106596371627789e-8, (12, 1) = -0.45148718532454525e-7, (12, 2) = -0.33200029720200515e-8, (12, 3) = 0.45977051212970705e-8, (13, 1) = -0.4644624587319399e-7, (13, 2) = -0.16812844515373377e-8, (13, 3) = 0.2476976139544679e-8, (14, 1) = -0.4728162048888603e-7, (14, 2) = -0.597980012160218e-9, (14, 3) = 0.10035287537696905e-8, (15, 1) = -0.4774964466124897e-7, (15, 2) = 0.1516792967540915e-10, (15, 3) = 0.1216447480458187e-9, (16, 1) = -0.4797098512847073e-7, (16, 2) = 0.2984480082832177e-9, (16, 3) = -0.32609332485037004e-9, (17, 1) = -0.4804804671209328e-7, (17, 2) = 0.3798012127372219e-9, (17, 3) = -0.497031217110049e-9, (18, 1) = -0.4805324175520197e-7, (18, 2) = 0.3535479474474593e-9, (18, 3) = -0.5125103792466736e-9, (19, 1) = -0.48031643002679316e-7, (19, 2) = 0.28054921031195175e-9, (19, 3) = -0.4535792419789312e-9, (20, 1) = -0.4800808931165307e-7, (20, 2) = 0.19581304022615792e-9, (20, 3) = -0.3686139862436758e-9, (21, 1) = -0.4799424116835274e-7, (21, 2) = 0.11696392107492342e-9, (21, 3) = -0.2833008145543955e-9, (22, 1) = -0.4799400195331907e-7, (22, 2) = 0.51123446927522176e-10, (22, 3) = -0.20919618553471444e-9, (23, 1) = -0.4800625077534693e-7, (23, 2) = .0, (23, 3) = -0.15020239214744807e-9}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[23] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(1.5281918615445138e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [3, 23, [F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(3, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(23, 3, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(3, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(23, 3, X, Y, outpoint, yout, L, V) end if; [xi = outpoint, seq('[F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)]'[i] = yout[i], i = 1 .. 3)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[23] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(1.5281918615445138e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [3, 23, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(23, 3, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(3, {(1) = 0., (2) = 0., (3) = 0.}); `dsolve/numeric/hermite`(23, 3, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 3)] end proc, (2) = Array(0..0, {}), (3) = [xi, F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [xi = res[1], seq('[F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)]'[i] = res[i+1], i = 1 .. 3)] catch: error  end try end proc

(7)

S11(0)

[xi = 0., F[0](xi) = HFloat(0.0), diff(F[0](xi), xi) = HFloat(0.5106187513453263), diff(diff(F[0](xi), xi), xi) = HFloat(-0.562177644962497)]

(8)

S11(inf)

[xi = 10., F[0](xi) = HFloat(0.42916939271150717), diff(F[0](xi), xi) = HFloat(0.0), diff(diff(F[0](xi), xi), xi) = HFloat(-1.9789658078119164e-6)]

(9)

NULL

NULL

inf := 4.2

equ4 := diff(f[1](eta), `$`(eta, 3))+theta[1](eta) = 0

equ5 := diff(theta[1](eta), `$`(eta, 2))+(3*1.88379445589794)*(diff(theta[1](eta), eta))+(3*(-0.182472319208178e-4))*f[1](eta) = 0

Bcs2 := f[1](0) = 0, (D(f[1]))(0) = 0, theta[1](0) = 0, theta[1](inf) = 0, (D(D(f[1])))(inf) = -.562177644962497

S2 := dsolve({Bcs2, equ4, equ5}, {f[1](eta), theta[1](eta)}, type = numeric)

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(11, {(1) = .0, (2) = .4116634332886109, (3) = .8886010476858462, (4) = 1.3528488149076092, (5) = 1.8045807366238487, (6) = 2.241555102796764, (7) = 2.6625695592004965, (8) = 3.0672725690885674, (9) = 3.4556665515316527, (10) = 3.831324258983187, (11) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(11, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -.5619986895834216, (1, 4) = .0, (1, 5) = 0.335774149965343e-3, (2, 1) = -0.4762032358997575e-1, (2, 2) = -.23135669488800123, (2, 3) = -.5620136602440209, (2, 4) = 0.53584183105081106e-4, (2, 5) = 0.3259167905984578e-4, (3, 1) = -.22188452637683598, (3, 2) = -.49940857560864915, (3, 3) = -.5620409665524415, (3, 4) = 0.58646668768565734e-4, (3, 5) = 0.7416150484543588e-6, (4, 1) = -.5143020373634434, (4, 2) = -.7603411477852857, (4, 3) = -.5620680774630706, (4, 4) = 0.5782030426624352e-4, (4, 5) = -0.3686352453447587e-5, (5, 1) = -.9151215778516861, (5, 2) = -1.0142510703826526, (5, 3) = -.5620937045204393, (5, 4) = 0.55371378860239725e-4, (5, 5) = -0.72839758029738255e-5, (6, 1) = -1.41198899414111, (6, 2) = -1.2598767815850975, (6, 3) = -.5621170728942686, (6, 4) = 0.51263362070545665e-4, (6, 5) = -0.11687120529486582e-4, (7, 1) = -1.9922344707360793, (7, 2) = -1.4965405780807717, (7, 3) = -.5621374727450006, (7, 4) = 0.4527873193435496e-4, (7, 5) = -0.16902962326608247e-4, (8, 1) = -2.643924136984444, (8, 2) = -1.7240428108976953, (8, 3) = -.5621542573727711, (8, 4) = 0.3726965687176117e-4, (8, 5) = -0.22825657629343497e-4, (9, 1) = -3.3559327840238864, (9, 2) = -1.9423827145168133, (9, 3) = -.5621668522332793, (9, 4) = 0.2716422553072306e-4, (9, 5) = -0.29348255430226227e-4, (10, 1) = -4.125270167459166, (10, 2) = -2.1535666676671648, (10, 3) = -.5621748236492027, (10, 4) = 0.14831645690104376e-4, (10, 5) = -0.3643841995320963e-4, (11, 1) = -4.957443956702882, (11, 2) = -2.3608275753757364, (11, 3) = -.562177644962497, (11, 4) = .0, (11, 5) = -0.4414396637606905e-4}, datatype = float[8], order = C_order); YP := Matrix(11, 5, {(1, 1) = .0, (1, 2) = -.5619986895834216, (1, 3) = -.0, (1, 4) = 0.335774149965343e-3, (1, 5) = -0.18975884465184773e-2, (2, 1) = -.23135669488800123, (2, 2) = -.5620136602440209, (2, 3) = -0.53584183105081106e-4, (2, 4) = 0.3259167905984578e-4, (2, 5) = -0.18679489023996156e-3, (3, 1) = -.49940857560864915, (3, 2) = -.5620409665524415, (3, 3) = -0.58646668768565734e-4, (3, 4) = 0.7416150484543588e-6, (3, 5) = -0.16337486187065928e-4, (4, 1) = -.7603411477852857, (4, 2) = -.5620680774630706, (4, 3) = -0.5782030426624352e-4, (4, 4) = -0.3686352453447587e-5, (4, 5) = -0.732077471409808e-5, (5, 1) = -1.0142510703826526, (5, 2) = -.5620937045204393, (5, 3) = -0.55371378860239725e-4, (5, 4) = -0.72839758029738255e-5, (5, 5) = -0.893076729232743e-5, (6, 1) = -1.2598767815850975, (6, 2) = -.5621170728942686, (6, 3) = -0.51263362070545665e-4, (6, 4) = -0.11687120529486582e-4, (6, 5) = -0.11246273353589229e-4, (7, 1) = -1.4965405780807717, (7, 2) = -.5621374727450006, (7, 3) = -0.4527873193435496e-4, (7, 4) = -0.16902962326608247e-4, (7, 5) = -0.13533173117094628e-4, (8, 1) = -1.7240428108976953, (8, 2) = -.5621542573727711, (8, 3) = -0.3726965687176117e-4, (8, 4) = -0.22825657629343497e-4, (8, 5) = -0.1573634882918884e-4, (9, 1) = -1.9423827145168133, (9, 2) = -.5621668522332793, (9, 3) = -0.2716422553072306e-4, (9, 4) = -0.29348255430226227e-4, (9, 5) = -0.17851208835849183e-4, (10, 1) = -2.1535666676671648, (10, 2) = -.5621748236492027, (10, 3) = -0.14831645690104376e-4, (10, 4) = -0.3643841995320963e-4, (10, 5) = -0.1989680395508565e-4, (11, 1) = -2.3608275753757364, (11, 2) = -.562177644962497, (11, 3) = -.0, (11, 4) = -0.4414396637606905e-4, (11, 5) = -0.2190441144981183e-4}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(11, {(1) = .0, (2) = .4116634332886109, (3) = .8886010476858462, (4) = 1.3528488149076092, (5) = 1.8045807366238487, (6) = 2.241555102796764, (7) = 2.6625695592004965, (8) = 3.0672725690885674, (9) = 3.4556665515316527, (10) = 3.831324258983187, (11) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(11, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.35508604778067024e-15, (1, 4) = .0, (1, 5) = 0.15397753328418554e-14, (2, 1) = 0.2558116197637096e-10, (2, 2) = -0.14456757081707498e-9, (2, 3) = 0.817011120093731e-9, (2, 4) = 0.4617236684306891e-8, (2, 5) = -0.2609377331174807e-7, (3, 1) = -0.9457936005633856e-11, (3, 2) = 0.5345381823058202e-10, (3, 3) = -0.30207991081338217e-9, (3, 4) = -0.1707174526030626e-8, (3, 5) = 0.9647899354096491e-8, (4, 1) = 0.2020346996825016e-11, (4, 2) = -0.11415519234215377e-10, (4, 3) = 0.6451847526201498e-10, (4, 4) = 0.3646134887612831e-9, (4, 5) = -0.2060569086207772e-8, (5, 1) = -0.17646929046515701e-12, (5, 2) = 0.10093169744755152e-11, (5, 3) = -0.5699389218375125e-11, (5, 4) = -0.3221591809328718e-10, (5, 5) = 0.18206604502968212e-9, (6, 1) = 0.8757302096159674e-14, (6, 2) = -0.3799530988879617e-13, (6, 3) = 0.2292287437287893e-12, (6, 4) = 0.12945323288954797e-11, (6, 5) = -0.731435866077949e-11, (7, 1) = -0.9110226200220738e-15, (7, 2) = 0.25567726327308368e-13, (7, 3) = -0.12993934244362953e-12, (7, 4) = -0.7335757077118738e-12, (7, 5) = 0.4147257410839353e-11, (8, 1) = 0.26358911697616852e-14, (8, 2) = 0.3882634055360638e-14, (8, 3) = -0.9480934215017551e-14, (8, 4) = -0.55231163150641485e-13, (8, 5) = 0.31367270612471335e-12, (9, 1) = 0.7629602722383346e-14, (9, 2) = 0.4396554488606655e-14, (9, 3) = -0.15992210754706523e-14, (9, 4) = -0.1230013855036495e-13, (9, 5) = 0.7105291182052132e-13, (10, 1) = 0.1485070353377911e-13, (10, 2) = 0.33969966675655985e-14, (10, 3) = -0.6675463903849193e-15, (10, 4) = -0.14924562287319862e-14, (10, 5) = 0.9974730177955179e-14, (11, 1) = 0.38908323477587536e-14, (11, 2) = 0.32750628566257692e-14, (11, 3) = .0, (11, 4) = .0, (11, 5) = 0.15404022343639915e-14}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[11] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.609377331174807e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 11, [f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[11] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[11] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(11, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(11, 5, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), eta)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[11] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.609377331174807e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 11, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[11] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[11] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(11, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(11, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(0..0, {}), (3) = [eta, f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [eta = res[1], seq('[f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), eta)]'[i] = res[i+1], i = 1 .. 5)] catch: error  end try end proc

(10)

S2(0)

[eta = 0., f[1](eta) = HFloat(0.0), diff(f[1](eta), eta) = HFloat(0.0), diff(diff(f[1](eta), eta), eta) = HFloat(-0.5619986895834218), theta[1](eta) = HFloat(0.0), diff(theta[1](eta), eta) = HFloat(3.3577414996534315e-4)]

(11)

S2(inf)

[eta = 4.2, f[1](eta) = HFloat(-4.95744395670288), diff(f[1](eta), eta) = HFloat(-2.3608275753757355), diff(diff(f[1](eta), eta), eta) = HFloat(-0.5621776449624968), theta[1](eta) = HFloat(0.0), diff(theta[1](eta), eta) = HFloat(-4.414396637606903e-5)]

(12)

"b:="

inf := 10

equ6 := diff(F[1](xi), `$`(xi, 3))-(4*.510618751345326)*(diff(F[1](xi), xi))+(3*(-.562177644962497))*F[1](0) = 0

diff(diff(diff(F[1](xi), xi), xi), xi)-2.042475005*(diff(F[1](xi), xi))-1.686532935*F[1](0) = 0

(13)

Bcs21 := F[1](0) = a, (D(F[1]))(0) = .510658709628757, (D(F[1]))(inf) = 0

F[1](0) = -.260972124, (D(F[1]))(0) = .510658709628757, (D(F[1]))(10) = 0

(14)

S21 := dsolve({Bcs21, equ6}, {F[1](xi)}, type = numeric)

Error, (in fproc) unable to store 'HFloat(1.0430076505022892)+1.686532935*F[1](0)' when datatype=float[8]

 

 

 

 


 

dsolve({Q(0) = 0, Q(t) = (1.375*4190)*(80-T__1(t)), Q(t) = (1.375*4190)*(T__2(t)-38.2), diff(Q(t), t) = (0.1375e-1*(T__1(t)-T__1s(t)))*((T__1(t)+T__1s(t))*(1/2)), diff(Q(t), t) = (0.1375e-1*(T__2s(t)-T__2(t)))*((T__2s(t)+T__2(t))*(1/2)), diff(Q(t), t) = (240*0.1375e-1)*(T__1s(t)-T__2s(t))/(0.1e-2)}, numeric)

Error, (in dsolve/numeric/DAE/initial) missing initial conditions for the following: {T__1s}

 

``

i got 3 diff ecuations with two algebraic ones. a system of DAEs. there is only a derivative included on systems, for which it's necesary only one initial condition for solving the system, which is Q(0)=0. why maple wants to know initial conditions for T_1s. it's not supposed to calculate it itself?
 

Download ecuation_2.mwecuation_2.mw

I try to solve numerically a boundary VP for ODE with different order of discontinuity of right part.

Say, the following BVP is given:

y''(x)+y'(x)+y(x)=F(x)

y(0)=1, y(2)=1

Let's use piecewise right part

F  := piecewise(x<=1, -x, x>1, 2*x+(x-1)^2)

plot(piecewise(x<=1, -x, x>1, 2*x+(x-1)^2), x=0..2,thickness=5)

The function

piecewise(x<=1, 1-x, x>1, (x-1)^2)

plot(piecewise(x<=1, 1-x, x>1, (x-1)^2), x=0..2, color=blue,thickness=5)

as obviuos, satisfies the BVP exclung the point x=1, where its 1st and 2nd derivatives are discontinuos.

Numerical solution

N0:=6:
As:=dsolve([diff(y(x), x$2)+diff(y(x), x)+y(x)=F,  y(0)=1, y(2)=1], y(x), type=numeric, output = Array([seq(2.0*k/N0, k=0..N0)]), 'maxmesh'=500, 'abserr'=1e-3):

provides the solution essentially different to exact one described above:

But if to use the right part

F := piecewise(x<=1, x^2+x+2, x>1, -x^2+x)

plot(piecewise(x<=1, x^2+x+2, x>1, -x^2+x), x=0..2, color=blue,thickness=5)

for which the function

piecewise(x<=1, 1-x+x^2, x>1, -1+3*x-x^2)

plot(piecewise(x<=1, 1-x+x^2, x>1, -1+3*x-x^2), x=0..2, thickness=5)

satisfies the BVP excluding x=1, where this function has discontinuity of 2nd derivative only, the corresponding numerical solution is very similar to this exact solution:

This reason of the difference between these two cases is clear. In the first case both 1st and 2nd derivatives are discontiuos, while in the second one -- 1st derivative is contiuos.

I wonder, if there are numerical methods, implemeted in Maple, for numerical solution of the first type BVP with non-smooth right part?

I am having difficulty to solve the following ODE

ode:=diff(R(x),x$6)=Dirac(x-y);

with initial and boundary conditions

bcs := ((D@@3)(R))(1) = 0, R(0)-((D@@5)(R))(0) = 0, ((D@@2)(R))(0)-((D@@3)(R))(0) = 0, ((D@@5)(R))(1) = 0, (D(R))(0)+((D@@4)(R))(0) = 0, ((D@@4)(R))(1) = 0;

I want to solve the above ODE for two cases 1) x>y and 2) x<=y

Thanks

 

Dear all,

I need to transforme these equation from time domain to frequency domain with fourier transforms and solve it in frequency domain but i received the flowing error

any helps

thank you !

 

``

restart:with(inttrans):

E:=1;L:=1;

1

 

1

(1)

 

equ := arccos(y(t)/R)*R*L*(diff(y(t), `$`(t, 1)))*abs(diff(y(t), `$`(t, 1)))+diff(y(t), `$`(t, 2))+m*sin(omega*t+k*R*sin(`&theta;l`))+arccos(y(t)/R);

arccos(y(t)/R)*R*(diff(y(t), t))*abs(diff(y(t), t))+diff(diff(y(t), t), t)+m*sin(omega*t+k*R*sin(`&theta;l`))+arccos(y(t)/R)

(2)

eq:=fourier(equ,t,omega);

((1/2)*I)*m*fourier(exp(-I*omega*t), t, omega)*exp(-(1/2)*k*R*exp(I*`&theta;l`)+(1/2)*k*R*exp(-I*`&theta;l`))-omega^2*fourier(y(t), t, omega)-((1/2)*I)*m*fourier(exp(I*omega*t), t, omega)*exp((1/2)*k*R*exp(I*`&theta;l`)-(1/2)*k*R*exp(-I*`&theta;l`))+R*fourier(arccos(y(t)/R)*(diff(y(t), t))*abs(diff(y(t), t)), t, omega)+fourier(arccos(y(t)/R), t, omega)

(3)

csi := y(0) = 0.2e-1, (D(y))(0) = 0;

y(0) = 0.2e-1, (D(y))(0) = 0

(4)

sol := dsolve({csi, eq}, numeric, maxfun = 1000000000)

Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)

 

Error, (in solve) cannot solve expressions with fourier(arccos(Y[1]/R)*YP[1]*abs(YP[1]), t, omega) for YP[1]

 

Code :

Download Fourier_TRAns_MAPLEprime.mwFourier_TRAns_MAPLEprime.mw

hi..

is correct this answer for differential equations??

i think order of result should be in (10^6 or 10^9 or higher) range....

please check it

thanks

hpp.mw
 

restart

L := 100*10^(-9):

Eq1 := {-(1017/1600000000000000000000000000000000000000000)*(diff(w(x), x, x, x, x, x, x))+(26169/40000000000000000000000000)*(diff(w(x), x, x, x, x))-0.8325000000e-4*omega^2+1.560937500*10^(-21)*omega^2*(diff(w(x), x, x)), w(0) = 0, w(1/10000000) = 0, (D(w))(0) = 0, (D(w))(1/10000000) = 0, ((D@@2)(w))(0) = 0, ((D@@2)(w))(1/10000000) = 0}:

sys := subs(omega^2 = omega2, Eq1);

{-(1017/1600000000000000000000000000000000000000000)*(diff(diff(diff(diff(diff(diff(w(x), x), x), x), x), x), x))+(26169/40000000000000000000000000)*(diff(diff(diff(diff(w(x), x), x), x), x))-0.8325000000e-4*omega2+0.1560937500e-20*omega2*(diff(diff(w(x), x), x)), w(0) = 0, w(1/10000000) = 0, (D(w))(0) = 0, (D(w))(1/10000000) = 0, ((D@@2)(w))(0) = 0, ((D@@2)(w))(1/10000000) = 0}

 

{-(5085/8)*(diff(diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), y))+6542250*(diff(diff(diff(diff(g1(y), y), y), y), y))-0.8325000000e-4*omega2+0.1560937500e-6*omega2*(diff(diff(g1(y), y), y)), 10000000*(D(g1))(0) = 0, 10000000*(D(g1))(1) = 0, 100000000000000*((D@@2)(g1))(0) = 0, 100000000000000*((D@@2)(g1))(1) = 0, g1(0) = 0, g1(1) = 0}

 

{-(5085/8)*(diff(diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), y))+6542250*(diff(diff(diff(diff(g1(y), y), y), y), y))-0.8325000000e-4*omega2+0.1560937500e-6*omega2*(diff(diff(g1(y), y), y))}, {10000000*(D(g1))(0) = 0, 10000000*(D(g1))(1) = 0, 100000000000000*((D@@2)(g1))(0) = 0, 100000000000000*((D@@2)(g1))(1) = 0, g1(0) = 0, g1(1) = 0}

 

{g1(0) = 0, g1(1) = 0, (D(g1))(0) = 0, (D(g1))(1) = 0, ((D@@2)(g1))(0) = 0, ((D@@2)(g1))(1) = 0}

 

{diff(diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), y), diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), diff(diff(diff(diff(g1(y), y), y), y), y), diff(diff(diff(g1(y), y), y), y), diff(diff(g1(y), y), y), diff(g1(y), y)}

 

{-(1017/1600000000000000000000000000000000000000000)*(diff(diff(diff(diff(diff(diff(w(x), x), x), x), x), x), x))+(26169/40000000000000000000000000)*(diff(diff(diff(diff(w(x), x), x), x), x))-0.8325000000e-4*omega2+0.1560937500e-20*omega2*(diff(diff(w(x), x), x))}

 

{-(5085/8)*(diff(diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), y))+6542250*(diff(diff(diff(diff(g1(y), y), y), y), y))-0.8325000000e-4*omega2+0.1560937500e-6*omega2*(diff(diff(g1(y), y), y))}

 

{diff(diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), y) = 10292.62537*(diff(diff(diff(diff(g1(y), y), y), y), y))-0.1309734513e-6*omega2+0.2455752212e-9*omega2*(diff(diff(g1(y), y), y))}

 

{diff(diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), y) = 10292.62537*(diff(diff(diff(diff(g1(y), y), y), y), y))-0.1309734513e13*omega3+2455752212.*omega3*(diff(diff(g1(y), y), y))}

 

{diff(diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), y) = 10292.62537*(diff(diff(diff(diff(g1(y), y), y), y), y))-0.1309734513e13*omega3+2455752212.*omega3*(diff(diff(g1(y), y), y)), g1(0) = 0, g1(1) = 0, (D(g1))(0) = 0, (D(g1))(1) = 0, ((D@@2)(g1))(0) = 0, ((D@@2)(g1))(1) = 0}

 

{((D@@3)(g1))(0), ((D@@3)(g1))(1), ((D@@4)(g1))(0), ((D@@4)(g1))(1), ((D@@5)(g1))(0), ((D@@5)(g1))(1)}

 

((D@@3)(g1))(0)

 

((D@@3)(g1))(1)

 

((D@@4)(g1))(0)

 

((D@@4)(g1))(1)

 

((D@@5)(g1))(0)

 

((D@@5)(g1))(1)

 

((D@@5)(g1))(1), ((D@@4)(g1))(0), ((D@@5)(g1))(0), ((D@@3)(g1))(1), ((D@@4)(g1))(1), ((D@@3)(g1))(0)

 

HFloat(-8.852947665097804e-24), HFloat(-8.991820290300328e-22), HFloat(8.852947665097804e-24), HFloat(-9.672787782157173e-20), HFloat(-8.991820290300328e-22), HFloat(9.672787782157165e-20)

(1)

sqrt(8.85294766509780*10^(-21)*10^19);

.2975390338

(2)

NULL


 

Download hpp.mw

 

Hello everyone,

I am trying to solve a system of ODE's numerically but the problem is with the condition f(0)+g(0)=1.

Here is the system with the initial conditions,

restart:
ode1:=diff(f(x), x,x)+(f(x)+g(x))*diff(f(x),x)=0;
ode2:=diff(g(x), x,x)+(f(x)+g(x))*diff(g(x),x)=0;
ics:=f(0)+g(0)=1,D(f)(0) =0,D(g)(0) =1;
dsolve({ode1,ode2,ics},numeric);

which give an error

Error, (in DEtools/convertsys) invalid specification of initial conditions

The above system is a simplified form of a very complicated one.

 

Hi,

do anybody know, how I can see how a function is programmed? I want to know more about dsolve function and what is hidden behind.

Thank you all

 

Hi,

Does anyone no how to normalize wavefunctions such that the plot on the right looks like the one on the left.

Here's my code:-

schro := {diff(psi(x), x, x)-(alpha*x^4+x^2-energy)*psi(x) = 0};

ic := {psi(3) = 0, (D(psi))(3) = 1};

Ic := [{psi(3) = 0, (D(psi))(3) = -1}, %$2];

E := [1.06538, 3.306, 5.74796];

schro1 := [seq(subs(energy = e, alpha = .1, schro), e = E)];

soln1 := [seq(dsolve(schro1[i] union Ic[i], {psi(x)}, type = numeric), i = 1 .. nops(E))]; with(plots);

display(seq(odeplot(soln1[i], [x, psi(x)], -3 .. 3, color = [red, blue, green][i]), i = 1 .. nops(E)))

 

Thanks in advance

Consider a simple differential equation:

f1 := t -> sin(t);
f2 := t -> cos(t);
dsys := {diff(x(t), t) = x(t)*f1(t)+f2(t), x(0) = 3};
solution_procedure := dsolve(dsys, type = numeric, output = listprocedure);

If initial condition is given like this: x(0)=3, then it compiles. But if I define x(0)=f1(3) then it gives an error:

Error, (in dsolve/numeric/process_input) invalid specification of initial conditions, got HFloat(3.0) = sin(3)

How can I handle this?

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